Coordinate Geometry Quizzes: Master Cartesian Coordinates, Lines, Circles, and More

Question 1

The coordinates of the point 3 units to the right and 2 units up from the origin are:

Accepted Answer

(3, 2)

Answer

(-3, 2)

Question 2

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

Accepted Answer

y = 3x + 1

Answer

y = 2x + 1

Answer

y = x + 3

Question 3

The radius of the circle with the equation (x - 2)^2 + (y + 1)^2 = 25 is:

Accepted Answer

5

Answer

12.5

Question 4

The distance between the points (2, 3) and (-1, 5) is:

Accepted Answer

2√5

Answer

4

Question 5

Which of the following equations represents a vertical line passing through the point (2, 5)?

Accepted Answer

x = 2

Answer

x = 5

Question 6

What is the gradient of the line that is perpendicular to the line with the equation y = 2x - 1?

Accepted Answer

-1/2

Answer

-2

Question 7

What is the area of a triangle with vertices at (0, 0), (3, 0), and (0, 4)?

Accepted Answer

6 square units

Answer

12 square units

Answer

18 square units

Answer

24 square units

Question 8

What is the slope of the line perpendicular to the line y = 2x - 3?

Accepted Answer

-1/2

Answer

1/2

Answer

2

Answer

-2

Question 9

What is the area of the circle with radius 3?

Accepted Answer

9π square units

Answer

12π square units

Answer

18π square units

Answer

27π square units

Question 10

Find the equation of the perpendicular bisector of the line segment joining the points (1, 2) and (5, 8).

Accepted Answer

y = -2x + 7

Answer

y = 2x - 3

Answer

y = x + 3

Answer

y = -x + 7

Question 11

Determine the equation of the circle with center (2, -3) and radius 5.

Accepted Answer

(x - 2)^2 + (y + 3)^2 = 25

Answer

(x - 2)^2 + (y + 3)^2 = 5

Answer

(x + 2)^2 + (y - 3)^2 = 25

Answer

(x + 2)^2 + (y - 3)^2 = 5

Question 12

Which line represents the equation y = 2x + 1?

Accepted Answer

A line passing through (0, 1) and (1, 3)

Answer

A circle with radius 1 centered at (0, 1)

Answer

A parabola opening upwards with vertex at (0, 1)

Answer

A hyperbola centered at (0, 1)

Question 13

Find the equation of the plane passing through the points (2, 3), (4, 7), and (6, 11).

Accepted Answer

2x + 3y = 13

Answer

2x - 3y = 1

Answer

x + 2y = 5

Answer

3x + 2y = 7

Question 14

Calculate the distance between the points A(3, 4) and B(7, 10).

Accepted Answer

8.06

Answer

12

Answer

5.66

Answer

10

Question 15

Find the area of the triangle with vertices A(2, 3), B(6, 7), and C(4, 9).

Accepted Answer

10.5

Answer

8

Answer

12

Question 16

Determine the equation of the line passing through the point (2, 3) with a slope of 2.

Accepted Answer

y = 2x - 1

Answer

y = x + 1

Answer

y = 3x - 2

Answer

y = -2x + 7

Question 17

Determine the radius of the circle with equation (x - 2)^2 + (y + 1)^2 = 16.

Accepted Answer

4

Answer

2

Answer

16

Answer

8

Question 18

In the Cartesian plane, the x-coordinate of a point is its horizontal position, while the y-coordinate is its vertical position. What are the coordinates of the point that lies 5 units to the right of the origin?

Accepted Answer

(5, 0)

Answer

(5, 5)

Answer

(-5, 0)

Answer

(0, 5)

Question 19

The slope of a line is a measure of its steepness. It is calculated as the ratio of the change in y to the change in x between two points on the line. What is the slope of the line passing through the points (1, 2) and (3, 6)?

Accepted Answer

2

Answer

1

Answer

3

Answer

-2

Question 20

Calculate the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3).

Accepted Answer

6 square units

Answer

4 square units

Answer

12 square units

Answer

3 square units

Question 21

In the equation of a line, y = mx + c, which variable represents the vertical intercept?

Accepted Answer

'c'

Answer

'y'

Answer

'm'

Answer

'x'

Question 22

A circle has a diameter of 10 units. Determine the length of its radius.

Accepted Answer

5 units

Answer

20 units

Answer

2.5 units

Answer

10 units

Question 23

Find the coordinates of the point where the line y = 2x - 1 intersects the x-axis.

Accepted Answer

(0.5, 0)

Answer

(1, 1)

Answer

(0, 2)

Answer

(-1, 1)

Question 24

Write the equation of the circle with center (2, -3) and radius 5.

Accepted Answer

(x - 2)² + (y + 3)² = 25

Answer

(x - 2)² + (y - 3)² = 25

Answer

(x + 2)² + (y - 3)² = 10

Answer

(x - 3)² + (y - 2)² = 25

Question 25

Calculate the distance between the points (3, 4) and (-1, 2).

Accepted Answer

5 units

Answer

6 units

Answer

10 units

Answer

4 units

Question 26

Find the area of the rectangle with vertices (0, 0), (6, 0), (0, 4), and (6, 4).

Accepted Answer

24 square units

Answer

30 square units

Answer

18 square units

Answer

12 square units

Question 27

Determine the midpoint of the line segment connecting the points (2, 5) and (8, 9).

Accepted Answer

(5, 7)

Answer

(4, 6)

Answer

(3, 4)

Answer

(6, 8)

Question 28

Calculate the gradient of the line passing through the points (2, 3) and (-1, 5).

Accepted Answer

-1/3

Answer

-3

Answer

1/3

Answer

3

Question 29

Which equation represents the line perpendicular to y = x + 2 and passing through the point (1, 3)?

Accepted Answer

y = -x + 4

Answer

y = x + 4

Answer

y = 2x + 1

Answer

y = -x + 2

Question 30

What is the area of a triangle with vertices (0, 0), (4, 0), and (0, 3)?

Accepted Answer

6

Answer

8

Answer

12

Answer

4