Coordinate Geometry Quizzes - Test Your Skills

Question 1

Find the equation of the circle with center at (-3, 4) and radius 5.

Accepted Answer

(x + 3)² + (y - 4)² = 25

Answer

(x - 3)² + (y - 4) = 5

Answer

(x + 3)² - (y - 4)² = 5

Answer

(x - 3)² - (y - 4)² = 25

Question 2

Determine the equation of a parabola with its vertex at (2, -3) and an axis of symmetry parallel to the y-axis.

Accepted Answer

y = (x - 2)^2 - 3

Answer

x = (y + 3)^2 - 2

Answer

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

Question 3

Find the equation of the circle with its center at (2, -1) and a radius of 4.

Accepted Answer

(x - 2)² + (y + 1)² = 16

Answer

(x - 4)² + (y + 1)² = 4

Answer

4(x - 2)² + 4(y + 1)² = 16

Answer

(x - 2)² - (y + 1)² = 4

Question 4

A farmer has a rectangular plot of land that measures 100 feet by 50 feet. He wants to fence the diagonal of the plot. How long will the fence be?

Accepted Answer

50√2 feet

Answer

100 feet

Answer

250 feet

Answer

150 feet

Question 5

What is the equation of a circle with center (-2, 3) and radius 4?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

Determine the equation of the circle with its center at (-2, 3) and a radius of 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 = 25

Answer

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

Question 7

Find the equation of the circle with its center at (-2, 3) and a radius of 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 = 5

Answer

(x - 2)² + (y + 3)² = 5

Question 8

What is the equation of the circle with a radius of 3 and a center at (2, 5)?

Accepted Answer

(x - 2)² + (y - 5)² = 3

Answer

(x - 2)² + (y - 5) = 3

Answer

(x + 2)² + (y - 5)² = 9

Answer

x² + y² = 3

Question 9

Find the equation of a circle with a radius of 5 and its center at the origin.

Accepted Answer

x^2 + y^2 = 25

Answer

x^2 - y^2 = 25

Answer

x + y = 25

Answer

x - y = 25

Question 10

Determine the equation of the circle with its center at (2, -1) and a radius of 3.

Accepted Answer

(x - 2)^2 + (y + 1)^2 = 3

Answer

(x + 2)^2 + (y - 1)^2 = 3

Answer

(x - 2)^2 + (y + 1)^2 = 9

Answer

(x + 2)^2 + (y - 1)^2 = 9

Question 11

Determine the equation of the parabola with a vertex at (1, 2) and a focus at (4, 2).

Accepted Answer

y = (x - 1)^2 + 2

Answer

y = (x + 1)^2 + 2

Answer

y = (x - 4)^2 + 2

Answer

y = (x + 4)^2 + 2

Question 12

What is the domain of the function f(x) = sqrt(x - 3)?

Accepted Answer

x ≥ 3

Answer

x < 3

Answer

x > 3

Answer

All real numbers

Question 13

What is the inverse of the function f(x) = 2x + 3?

Accepted Answer

f^(-1)(x) = (x - 3)/2

Answer

f^(-1)(x) = 2x - 3

Answer

f^(-1)(x) = -2x + 3

Answer

f^(-1)(x) does not exist

Question 14

For the circle defined by the equation (x - 3)^2 + (y + 1)^2 = 16, find its center coordinates and radius.

Accepted Answer

Center: (3, -1), Radius: 4

Answer

Center: (-3, 1), Radius: 16

Answer

Center: (3, 1), Radius: 16

Answer

Center: (-3, -1), Radius: 4

Question 15

Specify the domain of the function f(x) = sqrt(x - 3).

Accepted Answer

x ≥ 3

Answer

x > 3

Answer

x ≤ 3

Answer

x < 3

Question 16

Which equation represents a line with a slope of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

y = 2x - 3

Answer

y = 3x - 2

Question 17

Which equation represents a parabola with its vertex at (0, 0) and opens upwards?

Accepted Answer

y = x²

Answer

y = -x²

Answer

y = 2x²

Answer

y = -2x²

Question 18

Calculate the slope of a line perpendicular to the line y = 2x - 1?

Accepted Answer

-1/2

Answer

1/2

Answer

2

Answer

-2

Question 19

Which graph represents the inequality y < x + 2?

Accepted Answer

A shaded region below the line y = x + 2

Answer

A shaded region above the line y = x + 2

Answer

A shaded region to the left of the line y = x + 2

Answer

A shaded region to the right of the line y = x + 2

Question 20

Identify the center and radius of the circle represented by the equation (x - 1)² + (y + 2)² = 25.

Accepted Answer

Center: (1, 2), Radius: 5

Answer

Center: (1, -2), Radius: 5

Answer

Center: (-1, -2), Radius: 5

Answer

Center: (-1, 2), Radius: 5

Question 21

Which equation represents the parabola with vertex (2, 3) and focus (4, 3)?

Accepted Answer

y = (x - 2)² + 3

Answer

y = (x + 2)² + 3

Answer

y = (x - 4)² + 3

Answer

y = (x + 4)² + 3

Question 22

Determine the x-intercept of the circle represented by the equation x² + y² - 4x + 6y + 12 = 0.

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 23

Calculate the radius of the circle represented by the equation (x - 1)² + (y + 2)² = 25.

Accepted Answer

5

Answer

10

Answer

15

Answer

20

Question 24

Identify the equation of the line that is perpendicular to the line y = 2x + 3.

Accepted Answer

y = -1/2x + 1

Answer

y = -2x + 1

Answer

y = 2x - 1

Answer

y = 1/2x - 1

Question 25

Calculate the area of the rectangle defined by the vertices (0, 0), (3, 0), (3, 2), and (0, 2).

Accepted Answer

12

Answer

6

Answer

18

Answer

24

Question 26

Find the equation of the line passing through the point (2, -3) and parallel to the x-axis.

Accepted Answer

y = -3

Answer

y = 3

Answer

x = -3

Answer

x = 3

Question 27

Find the equation of the line passing through points (2, 5) and (-3, 11).

Accepted Answer

y = -x + 7

Answer

y = x + 3

Answer

y = 2x + 1

Question 28

Find the center (h, k) and radius (r) of the circle given by the equation: (x + 1)² + (y - 2)² = 4.

Accepted Answer

Center: (-1, 2); Radius: 2

Answer

Center: (0, -1); Radius: 4

Answer

Center: (1, -2); Radius: 1

Question 29

Find the equation of the parabola with vertex at (2, 3) that opens upward.

Accepted Answer

y = (x - 2)² + 3

Answer

y = (x + 2)² + 3

Answer

y = (x - 3)² + 2

Answer

y = (x + 3)² + 2

Question 30

Find the domain of the function f(x) = √(x + 4).

Accepted Answer

x ≥ 4

Answer

x ≤ 4

Answer

x > 4

Answer

x < 4

Question 31

Graph the inequality y > x - 1.

Accepted Answer

The region above the line y = x - 1

Answer

The region below the line y = x - 1

Answer

The line y = x - 1 itself

Answer

The entire coordinate plane

Question 32

Determine the equation of the parabola that has its vertex at the point (-1, 2) and opens downward.

Accepted Answer

y = -(x - 1)² - 2

Answer

y = (x + 1)² - 2

Answer

y = (x + 1)² + 2

Answer

y = -(x - 1)² + 2

Question 33

Determine the x-intercepts of the circle represented by the equation x^2 + y^2 = 25.

Accepted Answer

(-5, 0), (5, 0)

Answer

(-25, 0), (25, 0)

Answer

(0, -5), (0, 5)

Answer

(0, -25), (0, 25)

Question 34

Find the equation of the circle whose center is at (-2, 3) and whose radius is 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 = 5

Question 35

Find the radius of the circle represented by the equation x^2 + y^2 = 16.

Accepted Answer

4

Answer

2

Answer

16

Answer

8

Question 36

Locate the vertex of the parabola represented by the equation y = x^2 - 4x + 3.

Accepted Answer

(2, -1)

Answer

(-2, -1)

Answer

(1, 3)

Answer

(1, -3)

Question 37

Which of the following equations represents a line with a slope of -2 and a y-intercept of 3?

Accepted Answer

y = -2x + 3

Answer

y = 3x - 2

Answer

y = 2x + 3

Answer

y = -3x + 2

Question 38

Find the slope of the line perpendicular to the line with equation: y = -3x + 4

Accepted Answer

1/3

Answer

-3

Answer

-1/3

Answer

3

Question 39

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

Accepted Answer

(1, 4)

Answer

(-1, 4)

Answer

(4, -1)

Question 40

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

Accepted Answer

x^2 + y^2 = 9

Answer

x^2 - y^2 = 9

Answer

x^2 - y^2 = 3

Answer

x^2 + y^2 = 3

Question 41

Find the x-intercept of the line y = 2x - 4.

Accepted Answer

2

Answer

1

Answer

4

Answer

3

Question 42

Write the equation of the line with a slope of 2 and a y-intercept of -1.

Accepted Answer

y = 2x - 1

Answer

y = -2x + 1

Answer

y = -2x - 1

Answer

y = 2x + 1

Question 43

What is the equation of the perpendicular bisector of the line segment with endpoints (1, 2) and (3, 8)?

Accepted Answer

y = -1/2x + 5

Answer

y = 2x + 5

Answer

y = 1/2x + 5

Answer

y = -2x + 5

Question 44

Given the equation of a circle, x^2 + y^2 = r^2, which option correctly represents a circle with radius 5 and center at the origin?

Accepted Answer

x^2 + y^2 = 25

Answer

x + y = 5

Answer

x^2 + y^2 = 5

Answer

x - y = 25

Question 45

Determine the equation of the line perpendicular to y = 2x + 1 and passing through the point (3, 5).

Accepted Answer

y = -1/2x + 8/3

Answer

y = -2x + 1

Answer

y = 1/2x + 8/3

Answer

y = 2x + 4

Question 46

Identify the vertex of the parabola represented by the equation y = x^2 - 4x + 3.

Accepted Answer

(2, -1)

Answer

(0, 3)

Answer

(1, 4)

Answer

(4, -1)

Question 47

What is the equation of the perpendicular bisector of the line segment connecting the points (-1, 2) and (3, 4)?

Accepted Answer

y = -2x + 3

Answer

y = -2x - 3

Answer

y = 2x - 3

Answer

y = 2x + 3

Question 48

A line has a slope of -3 and passes through the point (0, 4). What is the equation of this line?

Accepted Answer

y = -3x + 4

Answer

y = 3x - 4

Answer

y = -3x - 4

Answer

y = 3x + 4

Question 49

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

Accepted Answer

5

Answer

4

Answer

6

Answer

8