If a point has coordinates (0, -4), where is it located?

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

If a point is located at (0, -4), where is it situated on the Cartesian plane?

Correct Option: B. Solution: A point with coordinates (0, -4) is located on the y-axis.

Coordinate Geometry

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CBSE Learning Objectives – Key Concepts & Skills You Must Know

Learning Objectives

Understand the concept of Coordinate Geometry.
Describe the position of a point in a plane using coordinates.
Identify the Cartesian system and its components (x-axis, y-axis, origin).
Explain the significance of quadrants in the Cartesian plane.
Calculate the coordinates of points based on their distances from the axes.
Differentiate between abscissa and ordinate.
Apply the Cartesian coordinate system to real-life situations, such as locating objects or places.

CBSE Revision Notes & Quick Summary for Last-Minute Study

Coordinate Geometry Notes

Introduction

The position of any object in a plane can be represented using two perpendicular lines (coordinate axes).
This concept is foundational in a branch of mathematics known as Coordinate Geometry, developed by René Descartes.

Cartesian System

The system for describing the position of a point in a plane is known as the Cartesian system.
It consists of:
- X-axis: Horizontal line
- Y-axis: Vertical line
- Origin: The intersection point of the axes, denoted as (0, 0).

Coordinates

A point's coordinates are expressed as (x, y), where:
- x-coordinate (abscissa): Distance from the Y-axis.
- y-coordinate (ordinate): Distance from the X-axis.
The coordinates of points on the axes are:
- X-axis: (x, 0)
- Y-axis: (0, y)

Quadrants

The coordinate plane is divided into four quadrants:
1. Quadrant I: (+, +)
2. Quadrant II: (-, +)
3. Quadrant III: (-, -)
4. Quadrant IV: (+, -)

Examples of Coordinates

Example of identifying coordinates:
- Point A at (4, 0): 4 units from the Y-axis, 0 from the X-axis.
- Point B at (0, 3): 0 from the X-axis, 3 units from the Y-axis.
- Point C at (-5, 0): -5 units from the Y-axis, 0 from the X-axis.

Summary of Key Points

To locate a point in a plane, two perpendicular lines are required.
The system of coordinates is a convention accepted globally to avoid confusion.
The coordinates of a point uniquely identify its position in the plane.

CBSE Exam Tips, Important Questions & Common Mistakes to Avoid

Common Mistakes and Exam Tips in Coordinate Geometry

Common Pitfalls

Misunderstanding Coordinates: Students often confuse the order of coordinates. Remember that the x-coordinate comes first, followed by the y-coordinate. For example, (3, 4) is not the same as (4, 3).
Quadrant Confusion: Students may forget the signs of coordinates in different quadrants.
- Quadrant I: (+, +)
- Quadrant II: (-, +)
- Quadrant III: (-, -)
- Quadrant IV: (+, -)
Origin Coordinates: Many forget that the coordinates of the origin are (0, 0).

Tips for Success

Practice with Graphs: Regularly practice plotting points on a Cartesian plane to become familiar with the coordinate system.
Use Visual Aids: Diagrams can help in understanding the relationship between coordinates and their respective quadrants.
Double-Check Coordinates: Always verify the signs of coordinates based on their quadrant before finalizing answers.

CBSE Quiz & Practice Test – MCQs, True/False Questions with Solutions

Multiple Choice Questions

x-axis

y-axis

Neither x-axis nor y-axis

Both x-axis and y-axis

Correct Answer: B

Solution:

A point with coordinates (0, y) lies on the y-axis. Since the x-coordinate is 0, the point (0, -4) lies on the y-axis.

(5, 9)

(9, 5)

(-5, 9)

(5, -9)

Correct Answer: A

Solution:

The point is 5 units away from the y-axis (x-coordinate) and 9 units above the x-axis (y-coordinate), so the coordinates are (5, 9).

(5, 2)

(2, 5)

(0, 0)

(5, 5)

Correct Answer: B

Solution:

The intersection is referred to as (2, 5), where 2 is the North-South street and 5 is the East-West street.

(3, 4)

(4, 3)

(3, 3)

(4, 4)

Correct Answer: A

Solution:

The coordinate system uses the format (North-South, East-West), so the intersection of the 3rd street North-South and 4th street East-West is (3, 4).

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

Correct Answer: B

Solution:

The point (-3, 5) has a negative x-coordinate and a positive y-coordinate, placing it in the second quadrant.

(-7, 5)

(-5, 7)

(7, 5)

(5, -7)

Correct Answer: A

Solution:

In the second quadrant, the x-coordinate is negative and the y-coordinate is positive. Therefore, the coordinates of

P

are (-7, 5).

x > 0, y > 0

x < 0, y > 0

x < 0, y < 0

x > 0, y < 0

Correct Answer: B

Solution:

In the second quadrant, the x-coordinate is negative, and the y-coordinate is positive, hence (x < 0, y > 0).

-2

Correct Answer: A

Solution:

The abscissa of a point is its x-coordinate. Therefore, the abscissa of the point (6, -2) is 6.

(5, 0)

(0, 5)

(-5, 0)

(0, -5)

Correct Answer: A

Solution:

A point located on the x-axis has a y-coordinate of 0. Therefore, the coordinates are (5, 0).

First Quadrant

Second Quadrant

Third Quadrant

Fourth Quadrant

Correct Answer: B

Solution:

The point (-3, 4) lies in the second quadrant where the x-coordinate is negative and the y-coordinate is positive.

(0, 5)

(5, 0)

(5, 5)

(0, -5)

Correct Answer: A

Solution:

The coordinates of a point on the y-axis 5 units above the origin are (0, 5).

4th row, 2nd column

2nd row, 4th column

4th column, 2nd row

2nd column, 4th row

Correct Answer: C

Solution:

In the given seating plan, the first number represents the column, and the second number represents the row.

On the x-axis

On the y-axis

In the first quadrant

In the fourth quadrant

Correct Answer: B

Solution:

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

x-axis

y-axis

Origin

None of the above

Correct Answer: A

Solution:

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

3rd street in the North-South direction, 4th street in the East-West direction

4th street in the North-South direction, 3rd street in the East-West direction

3rd street in the East-West direction, 4th street in the North-South direction

4th street in the East-West direction, 3rd street in the North-South direction

Correct Answer: A

Solution:

The first number in the pair (3, 4) refers to the street in the North-South direction, and the second number refers to the street in the East-West direction.

(3, 2)

(2, 3)

(3, 3)

(2, 2)

Correct Answer: A

Solution:

The position is represented by first writing the column number followed by the row number, so it is (3, 2).

(7, 3)

(3, 7)

(-7, 3)

(7, -3)

Correct Answer: A

Solution:

The point is 7 units away from the y-axis, so the x-coordinate is 7. It is 3 units above the x-axis, so the y-coordinate is 3. Therefore, the coordinates are (7, 3).

x-axis

y-axis

Origin

None of the above

Correct Answer: A

Solution:

The point (-5, 0) has a y-coordinate of 0, meaning it lies on the x-axis.

(5, 0)

(-5, 0)

(0, 5)

(0, -5)

Correct Answer: B

Solution:

A point on the x-axis has a y-coordinate of 0. If it is 5 units to the left of the origin, its x-coordinate is -5. Therefore, the coordinates are (-5, 0).

The y-coordinate is always positive.

The x-coordinate is always zero.

The y-coordinate is always zero.

Both coordinates are non-zero.

Correct Answer: C

Solution:

A point on the x-axis has a y-coordinate (ordinate) of zero because it lies on the horizontal axis. Therefore, the coordinates of any point on the x-axis are of the form

(x, 0)

. Hence, option C is correct.

2nd street from the North-South direction and 5th from the East-West direction

5th street from the North-South direction and 2nd from the East-West direction

2nd street from the East-West direction and 5th from the North-South direction

5th street from the East-West direction and 2nd from the North-South direction

Correct Answer: C

Solution:

The intersection (2, 5) indicates it is the 2nd street from the East-West direction and the 5th from the North-South direction, based on the convention described.

First Quadrant

Second Quadrant

Third Quadrant

Fourth Quadrant

Correct Answer: B

Solution:

The point (-5, 4) has a negative x-coordinate and a positive y-coordinate, placing it in the Second Quadrant.

First Quadrant

Second Quadrant

Third Quadrant

Fourth Quadrant

Correct Answer: B

Solution:

The point (-4, 5) has a negative x-coordinate and a positive y-coordinate, placing it in the Second Quadrant.

On the x-axis

On the y-axis

In the first quadrant

In the fourth quadrant

Correct Answer: B

Solution:

A point with coordinates (0, -4) is located on the y-axis.

(3, 4)

(4, 3)

(3, 3)

(4, 4)

Correct Answer: A

Solution:

Cross-streets are referred to by the North-South street number first, followed by the East-West street number, hence (3, 4).

x-axis

y-axis

Neither axis

Both axes

Correct Answer: A

Solution:

A point with coordinates (-3, 0) lies on the x-axis because its y-coordinate is 0.

x-axis

y-axis

Neither axis

Both axes

Correct Answer: B

Solution:

A point with coordinates (0, y) lies on the y-axis. Therefore, the point (0, -5) lies on the y-axis.

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

Correct Answer: D

Solution:

In the fourth quadrant, the x-coordinate is positive, and the y-coordinate is negative. Since the point (6, -2) has a positive x-coordinate and a negative y-coordinate, it lies in the fourth quadrant.

(2, 4)

(4, 2)

(2, 2)

(4, 4)

Correct Answer: B

Solution:

In a seating plan, the position is described by (column, row), so the coordinates are (4, 2).

Origin

Vertex

Intersection

Center

Correct Answer: A

Solution:

The point where the x-axis and y-axis intersect is called the origin, denoted as (0, 0).

(3, 4)

(4, 3)

(-4, -3)

(3, -4)

Correct Answer: B

Solution:

The point is 4 units from the y-axis and 3 units from the x-axis, so the coordinates are (4, 3).

(6, 0)

(0, 6)

(0, -6)

(-6, 0)

Correct Answer: A

Solution:

A point that is 6 units away from the y-axis and lies on the x-axis has coordinates (6, 0).

-6

Correct Answer: A

Solution:

The abscissa of a point is its x-coordinate, which is 6 for point D.

(3, -2)

(-3, 2)

(-3, -2)

(3, 2)

Correct Answer: B

Solution:

In the second quadrant, x-coordinates are negative and y-coordinates are positive, so (-3, 2) is in the second quadrant.

(3, -2)

(-3, -2)

(-3, 2)

(3, 2)

Correct Answer: B

Solution:

In the third quadrant, both x and y coordinates are negative, so (-3, -2) lies in the third quadrant.

(3, 4)

(4, 3)

(3, -4)

(-3, 4)

Correct Answer: A

Solution:

The coordinate representation of a point in this grid system is given as (North-South street number, East-West street number). Therefore, the point is represented as (3, 4).

x is positive, y is positive

x is negative, y is positive

x is negative, y is negative

x is positive, y is negative

Correct Answer: B

Solution:

In the second quadrant, the x-coordinate (abscissa) is negative and the y-coordinate (ordinate) is positive.

(3, 5)

(5, 3)

(3, 3)

(5, 5)

Correct Answer: B

Solution:

The position is given as (column, row), so the student's position is (5, 3).

(0, 0)

(1, 1)

(-1, -1)

(0, 1)

Correct Answer: A

Solution:

The origin is the point where both the x-axis and y-axis intersect, and its coordinates are (0, 0).

First Quadrant

Second Quadrant

Third Quadrant

Fourth Quadrant

Correct Answer: D

Solution:

The point (5, -3) has a positive x-coordinate and a negative y-coordinate, placing it in the Fourth Quadrant.

(4, 0)

(0, -3)

(2, 2)

(0, 0)

Correct Answer: B

Solution:

A point lies on the y-axis if its x-coordinate (abscissa) is zero. Thus, the point

(0, -3)

lies on the y-axis. Hence, option B is correct.

3rd street running North-South and 4th street running East-West

4th street running North-South and 3rd street running East-West

3rd street running East-West and 4th street running North-South

4th street running East-West and 3rd street running North-South

Correct Answer: A

Solution:

The convention used is that the first number represents the street running in the North-South direction and the second number represents the street running in the East-West direction.

(3, 2)

(2, 3)

(-3, 2)

(3, -2)

Correct Answer: A

Solution:

The point is 3 units to the right (positive x-direction) and 2 units above (positive y-direction), so the coordinates are (3, 2).

(3, -2)

(-3, 2)

(-3, -2)

(3, 2)

Correct Answer: A

Solution:

The point (3, -2) has a positive x-coordinate and a negative y-coordinate, placing it in the fourth quadrant.

(5, 9)

(9, 5)

(0, 0)

(9, 0)

Correct Answer: A

Solution:

The position of the dot is determined by its distances from the left edge and the bottom line, which are 5 cm and 9 cm respectively.

First Quadrant

Second Quadrant

Third Quadrant

Fourth Quadrant

Correct Answer: D

Solution:

In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative, which matches the point (4, -3).

P is in the first quadrant.

P is in the second quadrant.

P is in the third quadrant.

P is in the fourth quadrant.

Correct Answer: C

Solution:

Point P has both negative x and y coordinates, placing it in the third quadrant.

(3, 4)

(4, 3)

(-3, -4)

(-4, -3)

Correct Answer: A

Solution:

In the first quadrant, both

x

and

y

are positive. Since the point is 3 units away from the y-axis,

x = 3

. Since it is 4 units away from the x-axis,

y = 4

. Hence, the coordinates are (3, 4).

x > 0, y > 0

x < 0, y > 0

x < 0, y < 0

x > 0, y < 0

Correct Answer: C

Solution:

In the third quadrant, both x and y coordinates are negative, hence x < 0 and y < 0.

(0, 4)

(0, -4)

(4, 0)

(-4, 0)

Correct Answer: B

Solution:

A point on the y-axis has coordinates (0, y). If it is 4 units below the origin, the y-coordinate is -4, so the coordinates are (0, -4).

x-axis

y-axis

Neither axis

Both axes

Correct Answer: B

Solution:

The point (0, -5) lies on the y-axis since its x-coordinate is zero.

(-3, -5)

(3, 5)

(-3, 5)

(3, -5)

Correct Answer: D

Solution:

In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative. Therefore, the point (3, -5) lies in the fourth quadrant.

(3, -4)

(-3, -4)

(-3, 4)

(3, 4)

Correct Answer: B

Solution:

In the third quadrant, both the x-coordinate and y-coordinate are negative.

(5, -3)

(-4, 6)

(0, -7)

(7, 0)

Correct Answer: B

Solution:

A point in the second quadrant has a negative x-coordinate and a positive y-coordinate, such as (-4, 6).

-3

Correct Answer: B

Solution:

The ordinate is the y-coordinate of the point, which is -3.

(1, 0)

(0, 1)

(0, 0)

(1, 1)

Correct Answer: C

Solution:

The origin is the point where both the x-axis and y-axis intersect, which is at (0, 0).

Both

x

and

y

are positive.

Both

x

and

y

are negative.

x

is positive and

y

is negative.

x

is negative and

y

is positive.

Correct Answer: B

Solution:

In the third quadrant, both the x-coordinate (abscissa) and the y-coordinate (ordinate) are negative, hence the coordinates of a point in the third quadrant are of the form

(-, -)

. Therefore, option B is correct.

The student is in the 3rd row and 5th column.

The student is in the 5th row and 3rd column.

The student is in the 3rd row and 3rd column.

The student is in the 5th row and 5th column.

Correct Answer: B

Solution:

In a seating plan, the first number usually denotes the column and the second number denotes the row. Therefore, the position (3, 5) indicates that the student is sitting in the 5th row and 3rd column. Hence, option B is correct.

On the x-axis

On the y-axis

In the first quadrant

In the second quadrant

Correct Answer: B

Solution:

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

Row number

Column number

Desk number

None of the above

Correct Answer: B

Solution:

In the seating plan, the first number represents the column number, while the second number represents the row number.

-3

Correct Answer: B

Solution:

The abscissa is the x-coordinate of the point, which is 7.

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Correct Answer: B

Solution:

A point with coordinates (-3, 4) is located in Quadrant II, where the x-coordinate is negative and the y-coordinate is positive.

x-axis

y-axis

Neither

Both

Correct Answer: B

Solution:

The point (0, -6) has an x-coordinate of 0, meaning it lies on the y-axis.

True or False

Correct Answer: True

Solution:

In the first quadrant, both coordinates are positive. The point (3, 5) has positive x and y values, thus it lies in the first quadrant.

Correct Answer: False

Solution:

The point (3, 5) lies in the first quadrant of the Cartesian plane, where both x and y coordinates are positive.

Correct Answer: False

Solution:

To precisely locate a point on a plane, two independent pieces of information are required, such as distances from two perpendicular lines.

Correct Answer: False

Solution:

To describe the exact position of a point on a plane, two reference lines are necessary, such as the x-axis and y-axis.

Correct Answer: True

Solution:

René Déscartes developed the Cartesian coordinate system, which uses two perpendicular axes to describe the position of a point in a plane.

Correct Answer: True

Solution:

In coordinate geometry, a point's position is determined by its distances from two perpendicular lines, typically referred to as the x-axis and y-axis.

Correct Answer: True

Solution:

To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical.

Correct Answer: True

Solution:

René Déscartes is credited with developing the Cartesian coordinate system, which he conceptualized while resting in bed.

Correct Answer: True

Solution:

René Déscartes developed the Cartesian coordinate system, which uses two perpendicular lines to describe the position of a point in a plane.

Correct Answer: True

Solution:

In the Cartesian coordinate system, points in the third quadrant have both x and y coordinates negative, represented as (-, -).

Correct Answer: True

Solution:

René Déscartes developed the Cartesian coordinate system as a development of the older idea of latitude and longitude.

Correct Answer: True

Solution:

A point on the x-axis is characterized by having a y-coordinate of zero, which means it lies directly on the horizontal axis.

Correct Answer: False

Solution:

The coordinates of a point on the x-axis are of the form (x, 0) because the y-coordinate is always zero.

Correct Answer: True

Solution:

The axes divide the plane into four parts called quadrants, numbered I, II, III, and IV.

Correct Answer: False

Solution:

The origin of the Cartesian coordinate plane is located at (0, 0), where the x-axis and y-axis intersect.

Correct Answer: True

Solution:

Points on the y-axis have coordinates where the x-coordinate is zero, hence the form (0, y).

Correct Answer: True

Solution:

In coordinate geometry, two perpendicular lines, typically the x-axis and y-axis, are used to determine the position of a point in a plane.

Correct Answer: True

Solution:

The origin is the point where the x-axis and y-axis intersect, and it is denoted by the coordinates (0, 0).

Correct Answer: True

Solution:

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

Correct Answer: False

Solution:

In a seating plan, the position is described by the column number first, followed by the row number, as in (column, row).

Correct Answer: False

Solution:

Two perpendicular lines, the x-axis and y-axis, are needed to locate a point in a plane using the Cartesian system.

Correct Answer: True

Solution:

The y-coordinate (ordinate) of a point on the y-axis can be any real number, while the x-coordinate (abscissa) is zero.

Correct Answer: False

Solution:

To locate a point in a plane, two perpendicular lines are required: the x-axis and the y-axis. These lines allow us to determine the coordinates of the point, which are necessary for precise location.

Correct Answer: False

Solution:

In the second quadrant, the coordinates of a point are of the form (-, +).

Correct Answer: True

Solution:

The origin is the point where the x-axis and y-axis intersect, and it is located at (0, 0) in the Cartesian coordinate plane.

Correct Answer: True

Solution:

The x-coordinate, or abscissa, represents the distance of a point from the y-axis.

Correct Answer: False

Solution:

In the third quadrant, the coordinates of a point are of the form (-, -).

Coordinate Geometry

AI Learning Assistant

CBSE Learning Objectives – Key Concepts & Skills You Must Know

Learning Objectives

CBSE Revision Notes & Quick Summary for Last-Minute Study

Coordinate Geometry Notes

Introduction

Cartesian System

Coordinates

Quadrants

Examples of Coordinates

Summary of Key Points

CBSE Exam Tips, Important Questions & Common Mistakes to Avoid

Common Mistakes and Exam Tips in Coordinate Geometry

Common Pitfalls

Tips for Success

Multiple Choice Questions

Q1.If a point is located at (0, -4) on the Cartesian plane, which axis does it lie on?

Correct Answer: B

Q2.What are the coordinates of a point located 5 units away from the y-axis and 9 units above the x-axis?

Correct Answer: A

Q3.In a city grid, if the 2nd street running in the North-South direction intersects with the 5th street running in the East-West direction, what are the coordinates of this intersection?

Correct Answer: B

Q4.In a city grid, if the 3rd street running in the North-South direction intersects with the 4th street running in the East-West direction, what are the coordinates of this intersection?

Correct Answer: A

Q5.In the Cartesian plane, which quadrant does the point (-3, 5) lie in?

Correct Answer: B

Q6.A point PPP is located on a Cartesian plane such that it is 5 units away from the x-axis and 7 units away from the y-axis. If PPP lies in the second quadrant, what are the coordinates of PPP?

Correct Answer: A

Q7.In a coordinate plane, if a point is located at (x, y) and lies in the second quadrant, which of the following must be true?

Correct Answer: B

Q8.What is the abscissa of the point located at (6, -2)?

Correct Answer: A

Q9.What are the coordinates of a point located 5 units to the right of the origin on the x-axis?

Correct Answer: A

Q10.In a coordinate plane, if the coordinates of a point are (-3, 4), in which quadrant does the point lie?

Correct Answer: B

Q11.What are the coordinates of a point located on the y-axis 5 units above the origin?

Correct Answer: A

Q12.In a seating plan represented by a coordinate system, a student sits at (4, 2). Which of the following describes their position?

Correct Answer: C

Q13.If a point has coordinates (0, -4), where is it located?

Correct Answer: B

Q14.If a point has coordinates (x, 0), on which axis does it lie?

Correct Answer: A

Q15.If a city has streets running parallel to the x and y axes, and a cross-street is labeled as (3, 4), which of the following describes its position?

Correct Answer: A

Q16.In a classroom seating plan, if a student is sitting in the 3rd column and 2nd row, how would you represent their position?

Correct Answer: A

Q17.In a coordinate plane, a point is located at (x, y) where x is the distance from the y-axis and y is the distance from the x-axis. If a point is 7 units away from the y-axis and 3 units above the x-axis, what are its coordinates?

Correct Answer: A

Q18.If a point has coordinates (-5, 0), which axis does it lie on?

Correct Answer: A

Q19.What are the coordinates of a point that lies on the x-axis and is 5 units to the left of the origin?

Correct Answer: B

Q20.A point QQQ is located on the x-axis. Which of the following is true about the coordinates of QQQ?

Correct Answer: C

Q21.In a city grid, streets run parallel to the x and y axes. If a street intersection is labeled as (2, 5), which of the following accurately describes its position?

Correct Answer: C

Q22.Which quadrant does the point (-5, 4) lie in on the Cartesian coordinate plane?

Correct Answer: B

Q23.If a point is located at (-4, 5) on the Cartesian plane, in which quadrant does it lie?

Correct Answer: B

Q24.If a point is located at (0, -4), where is it situated on the Cartesian plane?

Correct Answer: B

Q25.In a city grid, streets run parallel to the main roads. If the 3rd street in the North-South direction and the 4th street in the East-West direction intersect, how is this cross-street referred to?

Correct Answer: A

Q26.If a point is located at (-3, 0) on the Cartesian plane, which axis does it lie on?

Correct Answer: A

Q27.If a point is located at (0, -5) on the Cartesian plane, on which axis does it lie?

Correct Answer: B

Q28.If a point is located at (6, -2) in the Cartesian plane, which quadrant does it lie in?

Correct Answer: D

Q29.In a seating plan, if a student is sitting in the 4th column and 2nd row, what are the coordinates of their position?

Correct Answer: B

Q30.What is the name of the point where the x-axis and y-axis intersect in a Cartesian coordinate plane?

Correct Answer: A

Q31.What are the coordinates of a point located 4 units from the y-axis and 3 units from the x-axis in the positive direction?

Correct Answer: B

Q32.What are the coordinates of a point that is 6 units away from the y-axis and lies on the x-axis?