Coordinate Geometry: Master the Basics with Interactive Quizzes

Question 1

Why are perpendicular bisectors of a line segment always perpendicular to that line segment?

Accepted Answer

Perpendicular bisectors are formed by reflecting the line segment over a line that is perpendicular to it.

Answer

The midpoint of a line segment always lies on its perpendicular bisector.

Answer

Perpendicular bisectors are parallel to the line segment they bisect.

Answer

The length of the perpendicular bisector is always equal to half the length of the line segment it bisects.

Question 2

Which of the following points lies on the line 2x + 3y = 6?

Accepted Answer

(2, 0)

Answer

(0, 2)

Answer

(1, 1)

Answer

(3, 0)

Question 3

What is the y-intercept of the line y = 2x + 1?

Accepted Answer

1

Answer

2

Answer

3

Question 4

Find the gradient of the line passing through the points (3, 4) and (-1, 2).

Accepted Answer

-1/2

Answer

1/2

Answer

-2

Answer

2

Question 5

Which of the following equations represents a line parallel to the x-axis?

Accepted Answer

y = 5

Answer

y = x + 2

Answer

y = 2x^2

Answer

y = -3x

Question 6

Find the equation of the circle with center (3, -2) and radius 4.

Accepted Answer

(x - 3)^2 + (y + 2)^2 = 16

Answer

(x + 3)^2 + (y - 2)^2 = 16

Answer

(x - 3)^2 + (y + 2)^2 = 4

Question 7

Find the area of the rectangle with vertices (0, 0), (5, 0), (5, 3), and (0, 3).

Accepted Answer

15 square units

Answer

10 square units

Answer

20 square units

Answer

25 square units

Question 8

Find the coordinates of the point that is 3 units to the right and 4 units up from the origin.

Accepted Answer

(3, 4)

Answer

(-3, 4)

Answer

(-3, -4)

Answer

(3, -4)

Question 9

What is the equation of the line that passes through the points (2, 3) and (4, 7)?

Accepted Answer

y = 2x + 1

Answer

y = x + 5

Answer

y = 2x - 1

Answer

y = x - 3

Question 10

What is the gradient of the line represented by the equation y = -3x + 5?

Accepted Answer

-3

Answer

-5

Answer

3

Answer

5

Question 11

Find the midpoint of the line segment joining the points (-2, 4) and (6, 10).

Accepted Answer

(2, 7)

Answer

(1, 2)

Answer

(4, 6)

Answer

(-4, 2)

Question 12

Identify the line that is parallel to the line y = 2x + 3.

Accepted Answer

y = 2x + 5

Answer

y = -2x + 5

Answer

y = x + 3

Answer

y = 2x - 1

Question 13

Find the coordinates of the midpoint of the line segment joining points A(1, 2) and B(3, 4).

Accepted Answer

(2, 3)

Answer

(2, 4)

Answer

(1, 3)

Answer

(3, 3)

Question 14

Determine the equation of the line that passes through point (2, 3) and is parallel to the **x-axis**.

Accepted Answer

y = 3

Answer

x = 2

Answer

y = 2x + 1

Answer

x = 3y - 1

Question 15

Find the gradient of the line passing through points (2, 5) and (4, 9).

Accepted Answer

2

Answer

1

Answer

-2

Answer

3

Question 16

Which equation represents a circle with a radius of 3 and its center at the origin?

Accepted Answer

x^2 + y^2 = 9

Answer

x + y = 9

Answer

x^2 - y^2 = 9

Answer

(x - 3)^2 + (y - 3)^2 = 9

Question 17

Find the coordinates of the point that is 3 units to the right and 5 units below the origin.

Accepted Answer

(3, -5)

Answer

(-5, 3)

Answer

(-3, 5)

Answer

(5, 3)

Question 18

Calculate the gradient of the line passing through the points (2, 3) and (5, 7).

Accepted Answer

4/3

Answer

-4/3

Answer

1/2

Answer

3/4

Question 19

Select the equation that represents a line with a gradient of 2 and a y-intercept of -3.

Accepted Answer

y = 2x - 3

Answer

x + 2y = 3

Answer

y = -2x + 3

Answer

x = 2y - 3

Question 20

Find the midpoint of the line segment joining the points (4, -2) and (8, 6).

Accepted Answer

(6, 2)

Answer

(12, 4)

Answer

(4, 4)

Answer

(6, -2)

Question 21

Find the distance between the points (2, 5) and (-3, 7).

Accepted Answer

√29

Answer

√36

Answer

√34

Answer

√20

Question 22

Find the area of the rectangle with vertices (0, 0), (3, 0), (3, 4), and (0, 4).

Accepted Answer

12 square units

Answer

6 square units

Answer

3 square units

Answer

9 square units

Question 23

Two lines are perpendicular if their gradients are...

Accepted Answer

Negative reciprocals

Answer

Reciprocal

Answer

Opposite

Answer

Equal

Question 24

The point (4, 2) lies on the line with equation y = mx + 1. Find the value of m.

Accepted Answer

1/4

Answer

-4

Answer

-1/4

Answer

4

Question 25

The line with equation y = -2x + 5 intersects the y-axis at the point...

Accepted Answer

(0, 5)

Answer

(0, 2.5)

Answer

(2.5, 0)

Answer

(5, 0)

Question 26

In the Cartesian coordinate system, which of the following ordered pairs represents the point located 3 units to the right of the origin and 4 units above the origin?

Accepted Answer

(3, 4)

Answer

(4, 3)

Answer

(-3, 4)

Answer

(3, -4)

Question 27

What is the gradient of a line that passes through the points (2, 3) and (4, 7)?

Accepted Answer

2

Answer

4

Answer

-2

Answer

0.5

Question 28

Which of the following equations represents a line that passes through the point (2, 3) and has a gradient of -2?

Accepted Answer

y = -2x + 7

Answer

y = 2x + 3

Answer

y = -2x + 3

Question 29

Find the midpoint of the line segment joining the points A(2, 5) and B(6, 11).

Accepted Answer

(4, 8)

Answer

(7, 13)

Answer

(5, 10)

Answer

(3, 6)

Question 30

What is the equation of the circle with center (-1, 3) and radius 4?

Accepted Answer

(x + 1)² + (y - 3)² = 16

Answer

(x + 1)² + (y - 3)² = 8

Answer

(x - 1)² + (y + 3)² = 4

Answer

(x - 1)² + (y + 3)² = 16

Question 31

Which of the following points lies on the line 2x - 3y = 6?

Accepted Answer

(3, 0)

Answer

(0, 3)

Answer

(4, 2)

Answer

(2, 4)

Question 32

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Accepted Answer

6

Answer

9

Answer

3

Answer

12

Question 33

What is the distance between the points (2, 3) and (6, 7)?

Accepted Answer

5

Answer

9

Answer

7

Answer

3

Question 34

Which of the following transformations would map the triangle with vertices (1, 2), (3, 2), and (3, 4) onto itself?

Accepted Answer

Rotation by 180° about the origin

Answer

Translation by 2 units to the right

Answer

Dilation by a factor of 2

Answer

Reflection in the y-axis

Question 35

What is the slope-intercept form of the line with equation 3x + 2y = 6?

Accepted Answer

y = -3/2x + 3

Answer

y = 2/3x + 3

Answer

y = -2/3x + 3

Answer

y = 3/2x + 3