Coordinate Geometry Quizzes: Master Cartesian Coordinates and Beyond

Question 1

The midpoint of line segment AB has coordinates (2, 5). If the coordinates of point A are (-1, 1), what are the coordinates of point B?

Accepted Answer

(5, 9)

Answer

(-5, 9)

Answer

(9, 5)

Question 2

Identify the domain of the function f(x) = sqrt(x - 2).

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 0

Answer

x ∈ R

Question 3

Which of the following inequalities represents the region of the Cartesian plane that lies to the left of the line x = 2?

Accepted Answer

x < 2

Answer

x > 2

Answer

y < 2

Answer

y > 2

Question 4

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

Accepted Answer

y = -x + 5

Answer

y = x + 1

Answer

y = x - 1

Answer

y = -x + 3

Question 5

Calculate the distance between points A(2, 3) and B(4, 7).

Accepted Answer

5

Answer

2

Answer

3

Answer

7

Question 6

Which transformation maps point A(2, 3) to point B(4, 3)?

Accepted Answer

Translation 2 units to the right

Answer

Translation 2 units to the left

Answer

Reflection in the x-axis

Answer

Rotation 180 degrees about the origin

Question 7

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

Accepted Answer

(2, 3)

Answer

(1, 3)

Answer

(3, 6)

Answer

(4, 6)

Question 8

Which inequality represents the region below the line with equation y = 2x + 1?

Accepted Answer

y ≤ 2x + 1

Answer

y ≥ 2x + 1

Answer

y < 2x + 1

Answer

y > 2x + 1

Question 9

Find the centre and radius of the circle with equation x^2 + y^2 = 25.

Accepted Answer

Centre: (0, 0), Radius: 5

Answer

Centre: (0, 5), Radius: 5

Answer

Centre: (5, 0), Radius: 5

Answer

Centre: (5, 5), Radius: 5

Question 10

Which transformation translates the point (3, 4) by 5 units to the right?

Accepted Answer

T(5, 0)

Answer

T(0, 5)

Answer

T(-5, 0)

Answer

T(0, -5)

Question 11

Find the midpoint of the line segment joining the points (2, 5) and (4, 7).

Accepted Answer

(3, 6)

Answer

(3, 12)

Answer

(6, 12)

Answer

(6, 6)

Question 12

Which line is perpendicular to the line y = 2x + 1?

Accepted Answer

y = -1/2x + 2

Answer

y = -2x + 3

Answer

y = 2x - 3

Answer

y = 1/2x - 2

Question 13

Which of the following is the equation of the line with a gradient of 2 passing through the point (1, 3)?

Accepted Answer

y = 2x + 1

Answer

y = x + 5

Answer

y = 2x - 1

Answer

y = 3x - 2

Question 14

Find the radius of the circle with equation x^2 + y^2 = 25.

Accepted Answer

5

Answer

10

Answer

15

Answer

20

Question 15

Determine the coordinates of the center of the circle with equation (x - 3)^2 + (y + 1)^2 = 9.

Accepted Answer

(3, 1)

Answer

(3, -1)

Answer

(-3, 1)

Answer

(-3, -1)

Question 16

What is the gradient of the line with the equation y = -2x + 3?

Accepted Answer

-2

Answer

2

Answer

-3

Answer

3

Question 17

Which of the following transformations maps the point (2, 3) to the point (6, 3)?

Accepted Answer

Translation 4 units right

Answer

Translation 4 units up

Answer

Reflection in the y-axis

Answer

Rotation 90 degrees clockwise about the origin

Question 18

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

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 19

Which of the following is the equation of the tangent to the circle with equation x^2 + y^2 = 25 at the point (3, 4)?

Accepted Answer

y = 4x - 7

Answer

y = -4x + 7

Answer

y = 3x + 4

Answer

y = -3x + 4

Question 20

In Cartesian coordinates, the point located 3 units right of the origin and 2 units above it has coordinates:

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(3, -2)

Answer

(2, -3)

Question 21

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

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = -3x + 2

Answer

y = 3x + 2

Question 22

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 23

Find the area of a triangle with vertices at (0, 0), (3, 4), and (6, 0).

Accepted Answer

12 square units

Answer

6 square units

Answer

18 square units

Answer

24 square units

Question 24

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

Accepted Answer

x^2 + y^2 = 9

Answer

x^2 - y^2 = 3

Answer

x^2 + y^2 = 3

Answer

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

Question 25

Which point lies on the circle with equation (x - 1)^2 + (y + 2)^2 = 9?

Accepted Answer

(3, 1)

Answer

(2, 0)

Answer

(0, -4)

Answer

(-1, 0)

Question 26

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

Accepted Answer

5

Answer

4

Answer

6

Question 27

Which of these points lies on the y-axis?

Accepted Answer

(0, 5)

Answer

(-2, -3)

Answer

(3, 4)

Answer

(5, 0)

Question 28

Which equation represents a line parallel to the x-axis?

Accepted Answer

y = 5

Answer

y = 2x + 1

Answer

x + y = 10

Answer

x - y = 3

Question 29

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

Accepted Answer

6

Answer

3

Answer

9

Answer

12

Question 30

Which point lies inside the circle defined by the equation  x² + y² ≤ 9?

Accepted Answer

(2, 1)

Answer

(0, -5)

Answer

(5, 6)

Answer

(-3, 4)

Question 31

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

Accepted Answer

2

Answer

1

Answer

-2

Answer

3

Question 32

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

Accepted Answer

y = 3x - 2

Answer

y = -3x - 2

Answer

y = -2x + 3

Answer

x = 3y - 2

Question 33

Which point is inside the circle with equation (x - 2)² + (y + 1)² = 25?

Accepted Answer

(3, 2)

Answer

(1, -1)

Answer

(-3, -2)

Answer

(5, 3)

Question 34

Which of the following is NOT a property of a rhombus?

Accepted Answer

It has four right angles

Answer

Its diagonals bisect each other at right angles

Answer

It has four equal sides

Answer

Its opposite sides are parallel

Question 35

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

Accepted Answer

A(2, 0)

Answer

B(0, 3)

Answer

C(-1, -2)

Answer

D(3, 4)

Question 36

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

Accepted Answer

-1/3

Answer

-3

Answer

3

Answer

1/3

Question 37

What is the equation of a line with a gradient of -2 and y-intercept of 5?

Accepted Answer

y = -2x + 5

Answer

y = 2x + 5

Answer

y = -5x + 2

Answer

y = 5x - 2

Question 38

Find the midpoint of the line segment joining points (3, 7) and (-5, 1).

Accepted Answer

(-1, 4)

Answer

(4, -8)

Answer

(-4, 8)

Question 39

Which of the following equations represents a circle with center (2, -1) and radius 3?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

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

Accepted Answer

12

Answer

18

Answer

6

Answer

24

Question 41

Which transformation would map the point (3, -2) onto the point (-3, 2)?

Accepted Answer

Reflection in the y-axis followed by a translation of 6 units to the left

Answer

Reflection in the x-axis followed by a translation of 6 units to the right

Answer

Rotation of 180 degrees about the origin

Question 42

Find the distance between the points (4, -3) and (-2, 5).

Accepted Answer

10

Answer

20

Answer

15

Answer

5

Question 43

Which of the following points is equidistant from the points (2, 3) and (-4, 1)?

Accepted Answer

(0, 2)

Answer

(1, 2)

Answer

(2, 0)

Answer

(-1, 2)

Question 44

A farmer has 100 meters of fencing to enclose a rectangular area. What is the maximum area he can enclose?

Accepted Answer

625 square meters

Answer

500 square meters

Answer

750 square meters

Answer

1000 square meters

Question 45

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

Accepted Answer

(0, 5)

Answer

(2, 0)

Answer

(5, 5)

Answer

(0, -3)

Question 46

Find the gradient of the line passing through the points (2, 3) and (4, 7).

Accepted Answer

2

Answer

4

Answer

1

Answer

0.5

Question 47

Which of the following equations represents a line with a gradient of -1 and y-intercept of 2?

Accepted Answer

y = -x + 2

Answer

y = -2x + 1

Answer

y = x - 2

Answer

y = 2x - 1

Question 48

Find the equation of the circle with centre (2, -1) and radius 3.

Accepted Answer

(x - 2)² + (y + 1)² = 9

Answer

(x + 2)² + (y + 1)² = 3

Answer

(x - 2)² + (y - 1)² = 3

Answer

(x + 2)² + (y - 1)² = 9

Question 49

Which of the following points is closest to the point (3, 4)?

Accepted Answer

(2, 5)

Answer

(1, 2)

Answer

(4, 6)

Answer

(5, 3)

Question 50

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

Accepted Answer

6

Answer

3

Answer

12

Answer

9

Question 51

Which of the following transformations maps the point (2, 3) to the point (6, 7)?

Accepted Answer

Translation by 4 units to the right and 4 units up

Answer

Reflection in the x-axis followed by a translation by 2 units to the right

Answer

Translation by 3 units to the left and 5 units up

Answer

Rotation by 90 degrees clockwise about the origin

Question 52

Find the coordinates of the midpoint of the line segment joining the points (1, 2) and (5, 6).

Accepted Answer

(3, 4)

Answer

(2, 3)

Answer

(6, 8)

Answer

(4, 5)

Question 53

Which of the following inequalities represents the shaded region below the line y = 2x + 1?

Accepted Answer

y ≤ 2x + 1

Answer

y < 2x + 1

Answer

y > 2x + 1

Answer

y ≥ 2x + 1

Question 54

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

Accepted Answer

2

Answer

1

Answer

3