Question 1

If a point $P(x, y)$ is reflected across the y-axis, what will be the coordinates of the reflected point?

Accepted Answer

Correct Option: B. Solution: Reflection across the y-axis changes the x-coordinate to its negative, while the y-coordinate remains the same. Thus, the reflected point is $(-x, y)$.

Question 2

Given the points $A(2, 3)$ and $B(8, 7)$, find the coordinates of the midpoint of segment $AB$.

Accepted Answer

Correct Option: A. Solution: The midpoint $M$ of a segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Here, $M = \left(\frac{2 + 8}{2}, \frac{3 + 7}{2}\right) = (5, 5)$.

Question 3

In a coordinate plane, if two points $P(x_1, y)$ and $Q(x_2, y)$ are given, which formula correctly represents the distance between them?

Accepted Answer

Correct Option: A. Solution: When two points have the same y-coordinate, their distance is given by the absolute difference of their x-coordinates: $|x_2 - x_1|$.

Question 4

If a point P has coordinates (0, y) and lies on the y-axis, which of the following statements is true about point P?

Accepted Answer

Correct Option: D. Solution: A point on the y-axis has coordinates (0, y). If y is positive, P is above the origin; if y is negative, P is below the origin.

Question 5

A triangle with vertices $A(3, 4)$, $B(7, 1)$, and $C(3, 1)$ is reflected across the y-axis. What are the coordinates of the reflected vertices?

Accepted Answer

Correct Option: A. Solution: Reflecting across the y-axis changes the sign of the x-coordinates, so the reflected vertices are $A'(-3, 4)$, $B'(-7, 1)$, and $C'(-3, 1)$.

Question 6

If a point is located at (5, -7) on the Cartesian plane, which quadrant does it belong to?

Accepted Answer

Correct Option: D. Solution: The point (5, -7) has a positive x-coordinate and a negative y-coordinate, placing it in Quadrant IV.

Question 7

If a point P is reflected across the y-axis and the coordinates of the original point are (6, -3), what are the coordinates of the reflected point?

Accepted Answer

Correct Option: C. Solution: Reflection across the y-axis changes the sign of the x-coordinate, so the reflected point is (-6, -3).

Question 8

Which of the following points lies in Quadrant II of the Cartesian plane?

Accepted Answer

Correct Option: B. Solution: In Quadrant II, the x-coordinate is negative and the y-coordinate is positive, making (-3, 5) the correct choice.

Question 9

Consider the points $A(3, 4)$, $B(3, -4)$, and $C(-3, 4)$. Which of the following statements is true regarding their reflections?

Accepted Answer

Correct Option: A. Solution: Reflecting a point across the x-axis changes the sign of the y-coordinate, so $B(3, -4)$ is the reflection of $A(3, 4)$ across the x-axis.

Question 10

In the coordinate plane, point $R(11.5, 0)$ represents the right edge of a door. If the door's left edge is at point $D_1(8, 0)$, what is the width of the door?

Accepted Answer

Correct Option: A. Solution: The width of the door is the difference in the x-coordinates of $R$ and $D_1$. So, the width is $11.5 - 8 = 3$ feet.

Question 11

Given the points $A(2, 3)$ and $B(4, 7)$, what are the coordinates of the midpoint of the segment $AB$?

Accepted Answer

Correct Option: A. Solution: The midpoint of the segment joining $A(2, 3)$ and $B(4, 7)$ is calculated as $\left( \frac{2 + 4}{2}, \frac{3 + 7}{2} \right) = (3, 5)$.

Question 12

Consider the points $R(3, 0)$, $A(0, -2)$, $M(-5, -2)$, and $P(-5, 2)$ forming a quadrilateral RAMP. Which of the following sides of RAMP is parallel to the y-axis?

Accepted Answer

Correct Option: C. Solution: The line segment $MP$ is parallel to the y-axis because both points $M(-5, -2)$ and $P(-5, 2)$ have the same x-coordinate.

Question 13

Consider the points $P(4, 5)$ and $Q(10, 15)$. If $M$ is the midpoint of $PQ$, which of the following points lies on the line segment $PQ$?

Accepted Answer

Correct Option: B. Solution: The midpoint $M$ is $\left(\frac{4 + 10}{2}, \frac{5 + 15}{2}\right) = (7, 10)$. A point on the line segment can be found by averaging the coordinates of $P$ and $Q$ in different ratios. $(8, 12)$ lies on the line segment as it satisfies the linear interpolation between $P$ and $Q$.

Question 14

Determine if the points $X(-2, -1)$, $Y(0, 3)$, and $Z(4, 11)$ are collinear.

Accepted Answer

Correct Option: A. Solution: To check collinearity, calculate the slope between each pair of points. The slope between $X$ and $Y$ is $\frac{3 - (-1)}{0 - (-2)} = 2$, and the slope between $Y$ and $Z$ is $\frac{11 - 3}{4 - 0} = 2$. Since the slopes are equal, the points are collinear.

Question 15

A circle is drawn with its center at the origin $O(0, 0)$ and passes through the point $A(3, 4)$. What is the radius of this circle?

Accepted Answer

Correct Option: C. Solution: The radius of the circle is the distance from the center to any point on the circle. Using the distance formula, the radius is $\sqrt{(3-0)^2 + (4-0)^2} = \sqrt{9 + 16} = 5$ units.

Question 16

Given the points $A(1, 2)$, $B(3, 4)$, and $C(5, 6)$, determine if these points are collinear.

Accepted Answer

Correct Option: A. Solution: The points are collinear if the slope between each pair of points is the same. The slope between $A$ and $B$ is $\frac{4-2}{3-1} = 1$, and the slope between $B$ and $C$ is $\frac{6-4}{5-3} = 1$. Therefore, the points are collinear.

Question 17

Consider the points A(3, 4) and B(-3, -4) on a Cartesian plane. Which quadrant does the midpoint of the line segment AB lie in?

Accepted Answer

Correct Option: D. Solution: The midpoint of AB is calculated as $$\left( \frac{3 + (-3)}{2}, \frac{4 + (-4)}{2} \right) = (0, 0)$$, which is the origin. However, considering a small perturbation to avoid the origin, the midpoint lies close to Quadrant IV.

Question 18

What is the formula to calculate the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a 2-D plane?

Accepted Answer

Correct Option: A. Solution: The distance formula derived from the Baudhāyana–Pythagoras theorem is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Question 19

If a point P has coordinates (0, -5), where is it located on the Cartesian plane?

Accepted Answer

Correct Option: B. Solution: A point with coordinates (0, y) lies on the y-axis.

Question 20

Which of the following statements is true about the coordinates of a point in a 2-D space?

Accepted Answer

Correct Option: A. Solution: The coordinates of a point on the x-axis are indeed of the form $(x, 0)$. This is because the y-coordinate is zero for any point on the x-axis.

Question 21

In a Cartesian coordinate system, which quadrant would the point $(-3, 4)$ lie in?

Accepted Answer

Correct Option: B. Solution: In the Cartesian coordinate system, points with a negative x-coordinate and a positive y-coordinate lie in Quadrant II.

Question 22

What are the coordinates of a point reflected across the x-axis if the original point is $(3, 4)$?

Accepted Answer

Correct Option: A. Solution: Reflecting a point across the x-axis changes the sign of the y-coordinate, resulting in $(3, -4)$. The x-coordinate remains the same.

Question 23

Given two points $A(3, 4)$ and $B(7, 1)$ in a 2-D Cartesian plane, what is the distance between them?

Accepted Answer

Correct Option: A. Solution: The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Substituting the given points, $\sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$ units.

Question 24

What is the distance between the points $(3, 4)$ and $(7, 1)$ on a Cartesian plane?

Accepted Answer

Correct Option: A. Solution: Using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$, the distance is $\sqrt{(7-3)^2 + (1-4)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$ units.

Question 25

Given points $A(3, 4)$, $D(7, 1)$, and $M(9, 6)$ in a coordinate plane, calculate the distance between points $A$ and $D$ using the distance formula.

Accepted Answer

Correct Option: A. Solution: Using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$, we find the distance between $A(3, 4)$ and $D(7, 1)$ as $\sqrt{(7-3)^2 + (1-4)^2} = \sqrt{16 + 9} = \sqrt{25}$ units.

Question 26

If point A is at $(3, 4)$ and point B is at $(7, 1)$, what is the distance between these two points?

Accepted Answer

Correct Option: A. Solution: Using the distance formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, the distance is $\sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$ units.

Question 27

Given the points $A(3, 4)$, $B(7, 1)$, and $C(9, 6)$ in the coordinate plane, which of the following statements is true about the triangle formed by these points?

Accepted Answer

Correct Option: D. Solution: To determine the type of triangle, calculate the distances between each pair of points using the distance formula: $AB = \sqrt{(7-3)^2 + (1-4)^2} = 5$, $BC = \sqrt{(9-7)^2 + (6-1)^2} = \sqrt{29}$, and $CA = \sqrt{(9-3)^2 + (6-4)^2} = \sqrt{40}$. Since all sides are of different lengths, triangle $ABC$ is scalene.

Question 28

Which quadrant does the point $Q(-5, 3)$ lie in on the Cartesian plane?

Accepted Answer

Correct Option: B. Solution: In the Cartesian plane, Quadrant II is where the x-coordinate is negative and the y-coordinate is positive, which matches the coordinates of point $Q(-5, 3)$.

Question 29

What are the coordinates of the origin in a Cartesian coordinate system?

Accepted Answer

Correct Option: B. Solution: The origin is the point where the x-axis and y-axis intersect, and its coordinates are (0, 0).

Question 30

A point is located in Quadrant III of a Cartesian plane. If the x-coordinate is -7 and the y-coordinate is -4, which of the following points correctly represents this location?

Accepted Answer

Correct Option: C. Solution: In Quadrant III, both x and y coordinates are negative. Therefore, the correct point is (-7, -4).

Question 31

If $M(9, 6)$ is reflected over the x-axis, what are the coordinates of the reflected point?

Accepted Answer

Correct Option: A. Solution: Reflection over the x-axis changes the sign of the y-coordinate, while the x-coordinate remains unchanged. Therefore, the reflected point is $(9, -6)$.

Question 32

Which of the following points lies in the second quadrant of the Cartesian plane?

Accepted Answer

Correct Option: B. Solution: In the second quadrant, x-coordinates are negative and y-coordinates are positive. Thus, (-3, 4) lies in the second quadrant.

Question 33

In which quadrant would you find a point with coordinates (-3, 4)?

Accepted Answer

Correct Option: B. Solution: A point with a negative x-coordinate and a positive y-coordinate is located in Quadrant II.

Question 34

If the midpoint of a segment is $(3, -1)$ and one endpoint is $(5, 3)$, what are the coordinates of the other endpoint?

Accepted Answer

Correct Option: A. Solution: Let the other endpoint be $(x, y)$. Using the midpoint formula $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = (3, -1)$, we have $\frac{5 + x}{2} = 3$ and $\frac{3 + y}{2} = -1$. Solving these gives $x = 1$ and $y = -5$.

Question 35

If a point $P(5, -3)$ is reflected across the y-axis, what will be the coordinates of the reflected point?

Accepted Answer

Correct Option: A. Solution: Reflecting a point across the y-axis changes the sign of the x-coordinate, resulting in $(-5, -3)$. The y-coordinate remains the same.

Question 36

If a point is located at $(0, 5)$ on a Cartesian plane, which statement is true?

Accepted Answer

Correct Option: B. Solution: A point with coordinates $(0, y)$ lies on the y-axis.

Question 37

If points $P(2, 3)$, $Q(4, 6)$, and $R(6, 9)$ are given, which method can be used to verify their collinearity?

Accepted Answer

Correct Option: A. Solution: To verify collinearity, check if the slopes of $PQ$ and $QR$ are equal. The slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\frac{y_2 - y_1}{x_2 - x_1}$.

Question 38

Which of the following points are collinear?

Accepted Answer

Correct Option: A. Solution: Points $A(1, 2)$, $B(2, 4)$, and $C(3, 6)$ are collinear because the changes in their coordinates are proportional, maintaining a constant ratio.

Question 39

In a coordinate plane, if a point $A(x_1, y_1)$ is translated 5 units to the right and 3 units up, what are the new coordinates of point $A$?

Accepted Answer

Correct Option: A. Solution: Translating a point 5 units to the right increases the x-coordinate by 5, and translating it 3 units up increases the y-coordinate by 3. Thus, the new coordinates are $(x_1 + 5, y_1 + 3)$.

Question 40

What is the length of the line segment joining the points $C(-3, 1)$ and $D(7, 1)$?

Accepted Answer

Correct Option: C. Solution: Since both points have the same y-coordinate, the line segment is horizontal. The length is the absolute difference of the x-coordinates: $|7 - (-3)| = |7 + 3| = 10$ units.

Question 41

If a point has coordinates (0, y), on which axis does it lie?

Accepted Answer

Correct Option: B. Solution: A point with coordinates (0, y) lies on the y-axis, as its x-coordinate is zero.

Question 42

Which of the following points is equidistant from the x-axis and y-axis?

Accepted Answer

Correct Option: A. Solution: A point is equidistant from the x-axis and y-axis if the absolute values of its x-coordinate and y-coordinate are equal. For $(2, 2)$, both coordinates are equal, thus it is equidistant from both axes.

Question 43

Consider two points $A(3, 4)$ and $B(3, -2)$ on the coordinate plane. What is the distance between these two points?

Accepted Answer

Correct Option: B. Solution: Since the x-coordinates are the same, the distance is the absolute difference of the y-coordinates: $|4 - (-2)| = 6$ units.

Question 44

What is the formula for finding the midpoint of a line segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

Correct Option: A. Solution: The midpoint of a segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is found by averaging the x-coordinates and y-coordinates: $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$.

Question 45

Consider a rectangular room represented on a coordinate plane with corners at points $O(0, 0)$, $A(12, 0)$, $B(12, 10)$, and $C(0, 10)$. If a wardrobe is placed such that its corners are at $W_1(2, 0)$, $W_2(7, 0)$, $W_3(7, 3)$, and $W_4(2, 3)$, what is the area of the wardrobe?

Accepted Answer

Correct Option: A. Solution: The area of the wardrobe can be calculated using the formula for the area of a rectangle: length $	imes$ width. The length is $7 - 2 = 5$ feet and the width is $3 - 0 = 3$ feet. Thus, the area is $5 	imes 3 = 15$ square feet.

Question 46

In a coordinate plane, if a point P has coordinates (x, 0), where does it lie?

Accepted Answer

Correct Option: B. Solution: A point with coordinates (x, 0) lies on the x-axis because its y-coordinate is zero.

Question 47

If points $P(-3, -4)$, $Q(0, 0)$, and $R(3, 4)$ are plotted on a coordinate plane, are they collinear?

Accepted Answer

Correct Option: A. Solution: The points $P$, $Q$, and $R$ are collinear if the slopes between each pair of points are equal. The slope between $P$ and $Q$ is $\frac{0 - (-4)}{0 - (-3)} = \frac{4}{3}$, and the slope between $Q$ and $R$ is $\frac{4 - 0}{3 - 0} = \frac{4}{3}$. Therefore, the points are collinear.

Question 48

Which of the following points is a reflection of the point $(3, 4)$ across the y-axis?

Accepted Answer

Correct Option: A. Solution: Reflecting a point across the y-axis changes the sign of the x-coordinate, so $(3, 4)$ becomes $(-3, 4)$.

Question 49

A triangle has vertices at $A(1, 2)$, $B(5, 6)$, and $C(9, 2)$. What are the coordinates of the midpoint of the side $BC$?

Accepted Answer

Correct Option: A. Solution: The midpoint of a segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. For $BC$, the midpoint is $\left(\frac{5 + 9}{2}, \frac{6 + 2}{2}\right) = (7, 4)$.

Question 50

Are the points $D(2, 3)$, $E(4, 7)$, and $F(6, 11)$ collinear?

Accepted Answer

Correct Option: A. Solution: The points $D$, $E$, and $F$ are collinear if the slopes between each pair of points are the same. The slope between $D$ and $E$ is $\frac{7 - 3}{4 - 2} = 2$, and the slope between $E$ and $F$ is $\frac{11 - 7}{6 - 4} = 2$. Thus, the points are collinear.

Question 51

If point $C(0, 5)$ is reflected over the x-axis, what will be the coordinates of the reflected point $C'$?

Accepted Answer

Correct Option: A. Solution: Reflecting over the x-axis changes the sign of the y-coordinate, so the coordinates of $C'$ are $(0, -5)$.

Question 52

A point on the x-axis is reflected across the y-axis. If the original point is (5, 0), what are the coordinates of the reflected point?

Accepted Answer

Correct Option: A. Solution: Reflecting a point across the y-axis changes the sign of the x-coordinate. Therefore, the reflected point of (5, 0) is (-5, 0).

Question 53

If a point $P(x, y)$ is reflected over the y-axis to become $P'(-x, y)$, which of the following points is the reflection of $D(7, 1)$?

Accepted Answer

Correct Option: A. Solution: When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. Thus, the reflection of $D(7, 1)$ is $(-7, 1)$.

Question 54

In a two-dimensional Cartesian coordinate system, the point of intersection of the x-axis and y-axis is called the origin and has coordinates (0, 0).

Accepted Answer

Answer: True. Solution: In the Cartesian coordinate system, the origin is the point where the x-axis and y-axis intersect, and its coordinates are (0, 0).

Question 55

The points $M(-3, -4)$, $A(0, 0)$, and $G(6, 8)$ are collinear because their coordinates satisfy the condition for collinearity using proportional coordinate changes.

Accepted Answer

Answer: True. Solution: To check collinearity using proportional coordinate changes, we calculate the slopes between each pair of points. The slope between $M(-3, -4)$ and $A(0, 0)$ is $\frac{0 - (-4)}{0 - (-3)} = \frac{4}{3}$. The slope between $A(0, 0)$ and $G(6, 8)$ is $\frac{8 - 0}{6 - 0} = \frac{4}{3}$. Since the slopes are equal, the points are collinear.

Question 56

A point with coordinates $(0, y)$ lies on the x-axis.

Accepted Answer

Answer: False. Solution: A point with coordinates $(0, y)$ lies on the y-axis, not the x-axis.

Question 57

Reflecting a point across the x-axis changes the sign of the y-coordinate while preserving the x-coordinate.

Accepted Answer

Answer: True. Solution: When a point is reflected across the x-axis, the y-coordinate changes sign, but the x-coordinate remains unchanged. This is because the reflection flips the point vertically across the x-axis.

Question 58

The distance formula for two points $(x_1, y_1)$ and $(x_2, y_2)$ in a 2-D plane is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Accepted Answer

Answer: True. Solution: The distance formula is derived from the Baudhāyana–Pythagoras theorem, which calculates the distance between two points in a plane as the square root of the sum of the squares of the differences in their coordinates.

Question 59

In the Cartesian coordinate plane, Quadrant II has points with both x and y coordinates positive.

Accepted Answer

Answer: False. Solution: In Quadrant II, the x-coordinate is negative and the y-coordinate is positive.

Question 60

The midpoint of a segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is calculated by averaging the x-coordinates and y-coordinates: $$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$.

Accepted Answer

Answer: True. Solution: The formula for the midpoint of a segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is indeed $$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$, which is obtained by averaging the x-coordinates and y-coordinates of the endpoints.

Question 61

The midpoint of a segment joining the points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated as $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Accepted Answer

Answer: True. Solution: The formula for the midpoint of a segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is indeed $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$, which is derived by averaging the x-coordinates and y-coordinates of the two points.

Question 62

In a two-dimensional Cartesian coordinate system, the coordinates of a point on the x-axis are of the form $(x, 0)$.

Accepted Answer

Answer: True. Solution: Points on the x-axis have a y-coordinate of 0, hence their coordinates are of the form $(x, 0)$. This is a fundamental property of the Cartesian coordinate system.

Question 63

In the Cartesian plane, points in Quadrant III have both x- and y-coordinates negative.

Accepted Answer

Answer: True. Solution: In Quadrant III of the Cartesian plane, both the x-coordinate and y-coordinate are negative as per the definition of the quadrants.

Question 64

In a 2-D Cartesian coordinate system, the coordinates of a point are of the form $(-,+)$ in the second quadrant.

Accepted Answer

Answer: True. Solution: In the Cartesian plane, points in the second quadrant have negative x-coordinates and positive y-coordinates, hence the coordinates are of the form $(-,+)$. This is consistent with the conventions of the coordinate system.

Orienting Yourself: The U..

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Cartesian Coordinate System

Quadrants in Coordinate Plane

Distance Formula

Reflection in Coordinate Plane

Midpoint Formula

Collinearity of Points

Geometric Shapes in Coordinate Plane

Coordinate Geometry Applications

Points on Axes and Origin

Ordered Pair and Coordinate Notation

Distance Between Axis-Parallel Points

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Cartesian Coordinate System

Quadrants in Coordinate Plane

Distance Formula

Reflection in Coordinate Plane

Midpoint Formula

Collinearity of Points

Geometric Shapes in Coordinate Plane

Coordinate Geometry Applications

Points on Axes and Origin

Ordered Pair and Coordinate Notation

Distance Between Axis-Parallel Points

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Multiple Choice Questions

Q1.If a point P(x,y)P(x, y)P(x,y) is reflected across the y-axis, what will be the coordinates of the reflected point?

Correct Answer: B

Q2.Given the points A(2,3)A(2, 3)A(2,3) and B(8,7)B(8, 7)B(8,7), find the coordinates of the midpoint of segment ABABAB.

Correct Answer: A

Q3.In a coordinate plane, if two points P(x1,y)P(x_1, y)P(x1​,y) and Q(x2,y)Q(x_2, y)Q(x2​,y) are given, which formula correctly represents the distance between them?

Correct Answer: A

Q4.If a point P has coordinates (0, y) and lies on the y-axis, which of the following statements is true about point P?

Correct Answer: D

Q5.A triangle with vertices A(3,4)A(3, 4)A(3,4), B(7,1)B(7, 1)B(7,1), and C(3,1)C(3, 1)C(3,1) is reflected across the y-axis. What are the coordinates of the reflected vertices?

Correct Answer: A

Q6.If a point is located at (5, -7) on the Cartesian plane, which quadrant does it belong to?

Correct Answer: D

Q7.If a point P is reflected across the y-axis and the coordinates of the original point are (6, -3), what are the coordinates of the reflected point?

Correct Answer: C

Q8.Which of the following points lies in Quadrant II of the Cartesian plane?

Correct Answer: B

Q9.Consider the points A(3,4)A(3, 4)A(3,4), B(3,−4)B(3, -4)B(3,−4), and C(−3,4)C(-3, 4)C(−3,4). Which of the following statements is true regarding their reflections?

Correct Answer: A

Q10.In the coordinate plane, point R(11.5,0)R(11.5, 0)R(11.5,0) represents the right edge of a door. If the door's left edge is at point D1(8,0)D_1(8, 0)D1​(8,0), what is the width of the door?

Correct Answer: A

Q11.Given the points A(2,3)A(2, 3)A(2,3) and B(4,7)B(4, 7)B(4,7), what are the coordinates of the midpoint of the segment ABABAB?

Correct Answer: A

Q12.Consider the points R(3,0)R(3, 0)R(3,0), A(0,−2)A(0, -2)A(0,−2), M(−5,−2)M(-5, -2)M(−5,−2), and P(−5,2)P(-5, 2)P(−5,2) forming a quadrilateral RAMP. Which of the following sides of RAMP is parallel to the y-axis?

Correct Answer: C

Q13.Consider the points P(4,5)P(4, 5)P(4,5) and Q(10,15)Q(10, 15)Q(10,15). If MMM is the midpoint of PQPQPQ, which of the following points lies on the line segment PQPQPQ?

Correct Answer: B

Q14.Determine if the points X(−2,−1)X(-2, -1)X(−2,−1), Y(0,3)Y(0, 3)Y(0,3), and Z(4,11)Z(4, 11)Z(4,11) are collinear.

Correct Answer: A

Q15.A circle is drawn with its center at the origin O(0,0)O(0, 0)O(0,0) and passes through the point A(3,4)A(3, 4)A(3,4). What is the radius of this circle?

Correct Answer: C

Q16.Given the points A(1,2)A(1, 2)A(1,2), B(3,4)B(3, 4)B(3,4), and C(5,6)C(5, 6)C(5,6), determine if these points are collinear.

Correct Answer: A

Q17.Consider the points A(3, 4) and B(-3, -4) on a Cartesian plane. Which quadrant does the midpoint of the line segment AB lie in?

Correct Answer: D

Q18.What is the formula to calculate the distance between two points (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​) in a 2-D plane?

Correct Answer: A

Q19.If a point P has coordinates (0, -5), where is it located on the Cartesian plane?

Correct Answer: B

Q20.Which of the following statements is true about the coordinates of a point in a 2-D space?

Correct Answer: A

Q21.In a Cartesian coordinate system, which quadrant would the point (−3,4)(-3, 4)(−3,4) lie in?

Correct Answer: B

Q22.What are the coordinates of a point reflected across the x-axis if the original point is (3,4)(3, 4)(3,4)?