Coordinate Geometry Quizzes: Master Geometry with Coordinates

Question 1

Which point lies on the y-axis?

Accepted Answer

(3, 0)

Answer

(0, 3)

Answer

(4, 5)

Answer

(7, -2)

Question 2

Calculate the distance between points A(2, 5) and B(7, 11).

Accepted Answer

13 units

Answer

5 units

Answer

7 units

Answer

10 units

Question 3

Which transformation results in a dilation by a factor of 2?

Accepted Answer

(x, y) --> (2x, 2y)

Answer

(x, y) --> (x/2, y/2)

Answer

(x, y) --> (-2x, -2y)

Answer

(x, y) --> (1/2x, 1/2y)

Question 4

Determine the slope of the line passing through points (3, 4) and (7, 10).

Accepted Answer

3

Answer

1

Answer

1/3

Answer

3/1

Question 5

Find the equation of the line perpendicular to y = -2x + 3 and passing through point (4, 1).

Accepted Answer

y = -(1/2)x + 5

Answer

y = (1/2)x + 5

Answer

y = 2x - 3

Answer

y = -2x - 3

Question 6

Calculate the distance between points (2, 3) and (-1, 5).

Accepted Answer

8 units

Answer

2 units

Answer

3 units

Answer

5 units

Question 7

Which equation represents a horizontal line?

Accepted Answer

y = 2

Answer

x = -3

Answer

y = mx + b

Answer

x^2 + y^2 = r^2

Question 8

Write the equation of the line through point (3, -2) with a slope of 1/2.

Accepted Answer

y = (1/2)x - 2

Answer

y = (1/2)x - 5

Answer

y = 2x - 5

Answer

y = 2x - 2

Question 9

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

Accepted Answer

13

Answer

2

Answer

5

Answer

10

Question 10

Determine the gradient (slope) of the line passing through the points (1, 2) and (3, 8).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 11

What is the equation of the line with a gradient (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 12

Determine if the points (1, 2), (3, 4), and (5, 6) are collinear (lie on the same line).

Accepted Answer

Yes

Answer

No

Answer

Cannot be determined

Question 13

What are the coordinates of the point that lies 3 units right and 2 units above the origin?

Accepted Answer

(3, 2)

Answer

(-3, -2)

Answer

(-2, 3)

Answer

(2, -3)

Question 14

Which equation represents a 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 15

Find the intersection point of the lines y = 2x - 1 and y = x + 3.

Accepted Answer

(2, 3)

Answer

(1, 1)

Answer

(3, 5)

Answer

(-1, -3)

Question 16

Which transformation will move a point 5 units right?

Accepted Answer

Translation: (x, y) -> (x + 5, y)

Answer

Translation: (x, y) -> (x - 5, y)

Answer

Reflection: y-axis

Answer

Rotation: 90 degrees clockwise

Question 17

Which of the points below lies on the x-axis?

Accepted Answer

(1, 0)

Answer

(0, 1)

Answer

(1, 1)

Answer

(0, 0)

Question 18

What is the x-intercept of the line y = 2x - 4?

Accepted Answer

(2, 0)

Answer

(0, -4)

Answer

(0, 4)

Answer

(-2, 0)

Question 19

Which of the following graphs represents the equation y = x^2 + 2x - 3?

Accepted Answer

A parabola opening upward

Answer

A parabola opening downward

Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Question 20

What is the domain of the function f(x) = sqrt(x - 1)?

Accepted Answer

x ≥ 1

Answer

x ≥ 0

Answer

x ≤ 0

Answer

x ≤ 1

Question 21

Which transformation maps the triangle with vertices (0,0), (3,0), and (0,4) onto the triangle with vertices (2,3), (5,3), and (2,6)?

Accepted Answer

Translation (2, 3)

Answer

Rotation of 90 degrees about the origin

Answer

Reflection over the y-axis

Answer

Dilation by a factor of 2

Question 22

Find the inverse of the linear function f(x) = 3x - 2.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

Are the points A(2, 1), B(4, 3), and C(6, 5) on the same line?

Accepted Answer

Yes

Answer

No

Answer

Cannot be determined

Question 24

Which of the following equations represents a line that passes through the point (3, 4) and has a slope of -2?

Accepted Answer

y = -2x + 10

Answer

y = -2x + 2

Answer

y = 2x + 10

Answer

y = 2x + 2

Question 25

What is the center of the circle with the equation (x - 3)^2 + (y + 1)^2 = 16?

Accepted Answer

(3, 1)

Answer

(0, 0)

Answer

(3, -1)

Answer

(-3, 1)

Question 26

What is the equation of the line perpendicular to the line y = 2x + 1 and passes through the point (2, 5)?

Accepted Answer

y = -1/2x + 6

Answer

y = 1/2x + 3

Answer

y = 2x - 1

Answer

y = -2x + 1

Question 27

What is the domain of the function f(x) = sqrt(x - 2)?

Accepted Answer

[2, ∞)

Answer

[0, ∞)

Answer

(-∞, 2]

Answer

(-∞, ∞)

Question 28

Which of the following points lies on the x-axis?

Accepted Answer

(3, 0)

Answer

(0, 2)

Answer

(-1, 3)

Answer

(2, -1)

Question 29

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

Accepted Answer

(x - 2)² + (y + 3)² = 16

Answer

(x + 2)² + (y - 3)² = 8

Answer

(x - 2)² + (y + 3)² = 4

Answer

(x + 2)² + (y - 3)² = 16

Question 30

Find the x-intercept of the line 2x + 3y = 6.

Accepted Answer

3

Answer

6

Answer

9

Answer

-3

Question 31

Which of the following equations represents a vertical line?

Accepted Answer

x = 2

Answer

y = 3

Answer

y = 2x + 1

Answer

x^2 + y^2 = 25

Question 32

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

Accepted Answer

6

Answer

12

Answer

18

Answer

24

Question 33

Which of the following inequalities represents the shaded region below the line y = x + 2?

Accepted Answer

y < x + 2

Answer

y > x + 2

Answer

y ≤ x + 2

Answer

y ≥ x + 2

Question 34

Find the midpoint of the line segment connecting the points (1,5) and (7,1).

Accepted Answer

(4,3)

Answer

(4,6)

Answer

(6,3)

Answer

(6,6)

Question 35

Which of these is the equation of a line parallel to the y-axis that passes through the point (3,-2)?

Accepted Answer

x = 3

Answer

y = 3

Answer

x = -2

Answer

y = -2

Question 36

Identify the center of the circle represented by the equation x^2 + y^2 = 25.

Accepted Answer

(0, 0)

Answer

(5, 0)

Answer

(0, 5)

Answer

(5, 5)

Question 37

Select the graph that represents the inequality y > 2x - 1.

Accepted Answer

Image of a shaded half-plane above a line

Answer

Image of a shaded half-plane below a line

Answer

Image of a shaded half-plane to the left of a line

Answer

Image of a shaded half-plane to the right of a line

Question 38

Determine the equation of the circle that passes through the points (2, 3), (4, 5), and (6, 3).

Accepted Answer

x^2 + (y - 3)^2 = 10

Answer

x^2 + y^2 = 10

Answer

x^2 + y^2 - 10x = 0

Answer

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

Question 39

Which point lies on the x-axis?

Accepted Answer

(-4, 0)

Answer

(2, 5)

Answer

(0, 3)

Answer

(0, -2)

Question 40

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = 2x - 3

Answer

y = 3x - 2

Answer

y = 3x + 2

Question 41

What is the center of the circle with equation (x - 2)^2 + (y + 1)^2 = 16?

Accepted Answer

(2, 1)

Answer

(-2, -1)

Answer

(2, -1)

Answer

(-2, 1)

Question 42

Graph the inequality y < x + 2.

Accepted Answer

A region below the line y = x + 2

Answer

A region above the line y = x + 2

Answer

A region left of the line y = x + 2

Answer

A region right of the line y = x + 2

Question 43

What is the slope of the line perpendicular to the line with equation 2x - y = 5?

Accepted Answer

-1/2

Answer

1/2

Answer

2

Answer

-2

Question 44

Which of the following points lies on the x-axis?

Accepted Answer

(2, 0)

Answer

(-1, -3)

Answer

(0, 3)

Answer

(2, 5)

Question 45

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

Accepted Answer

y = 5

Answer

2x - y = 1

Answer

y = -x + 7

Answer

y = x^2 - 3

Question 46

Which of the following is the equation of the circle with center (0, 0) and radius 5?

Accepted Answer

x^2 + y^2 = 25

Answer

(x + 5)^2 + (y + 5)^2 = 25

Answer

x^2 - y^2 = 25

Answer

(x - 5)^2 + (y - 5)^2 = 25

Question 47

Which of the following is the domain of the relation {(1, 2), (3, 4), (5, 6)}?

Accepted Answer

{1, 3, 5}

Answer

{1, 2, 3, 4, 5, 6}

Answer

{2, 4, 6}

Question 48

Find the inverse of the function f(x) = 2x + 1.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 49

Which of the following equations represents a line perpendicular to the line y = 2x + 3?

Accepted Answer

y = -1/2x - 1

Answer

y = -2x + 2

Answer

y = 2x - 1

Answer

y = 1/2x + 5

Question 50

Calculate the slope of a line that passes through the points (4, -1) and (8, 5).

Accepted Answer

3/2

Answer

2/3

Answer

-3/2

Answer

-2/3

Question 51

Write down the equation of a circle with center (2, -5) and radius 6.

Accepted Answer

(x - 2)² + (y + 5)² = 36

Answer

(x + 2)² + (y - 5)² = 36

Answer

(x - 2)² + (y + 5)² = 6

Question 52

Find the midpoint of the line segment joining the points A(-3, 2) and B(5, -6).

Accepted Answer

(1, -2)

Answer

(-4, 4)

Answer

(-1, 2)

Answer

(4, -4)

Question 53

Check if the point (6, 2) lies on the line 2x - 3y = 6.

Accepted Answer

Yes

Answer

No