Coordinate Geometry: Master the Coordinate Plane and Graphing

Question 1

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

Accepted Answer

10√2

Answer

5√2

Answer

10

Answer

20

Question 2

Determine the slope of the line represented by the equation 2x - 3y = 6.

Accepted Answer

-2/3

Answer

2/3

Answer

3/2

Answer

-3/2

Question 3

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

Accepted Answer

5

Answer

2

Answer

4

Answer

6

Question 4

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

Accepted Answer

(4, 3)

Answer

(3, 3)

Answer

(4, 6)

Answer

(6, 3)

Question 5

Determine the equation of the perpendicular bisector of the line segment connecting points (2, 5) and (6, 1).

Accepted Answer

y = -1/2x + 4

Answer

y = 1/2x + 2

Answer

y = -2x + 9

Answer

y = 2x - 1

Question 6

In the coordinate plane, the point that represents the origin (0, 0) is:

Accepted Answer

(0, 0)

Answer

(0, 1)

Answer

(1, 0)

Answer

(1, 1)

Question 7

Which of the following graphs represents the linear equation y = 2x + 1?

Accepted Answer

A line passing through (0, 1) with a slope of 2

Answer

A line passing through (1, 0) with a slope of 2

Answer

A line passing through (0, 0) with a slope of 2

Answer

A circle passing through (0, 1) with a radius of 1

Question 8

Which transformation maps the point (2, 3) to (6, 9)?

Accepted Answer

Translation 4 units right and 6 units up

Answer

Translation 6 units right and 4 units up

Answer

Reflection over the x-axis and translation 4 units right

Answer

Reflection over the y-axis and translation 6 units up

Question 9

Consider the line that passes through the points (2, 5) and (8, 1). Which of the following points is located on this line?

Accepted Answer

(4, 3)

Answer

(6, 2)

Answer

(10, 0)

Answer

(12, -2)

Question 10

Find the slope of the line represented by the equation 2x + 3y = 6.

Accepted Answer

2/3

Answer

-2/3

Answer

3/2

Answer

-3/2

Question 11

Identify the linear equation.

Accepted Answer

y = 2x + 1

Answer

y = x^2

Answer

y = sin(x)

Answer

y = e^x

Question 12

Which of the following equations represents a line passing through the points (2, 3) and (5, 7)?

Accepted Answer

y = 2x + 1

Answer

y = x + 1

Answer

y = 2x - 1

Answer

y = x - 2

Question 13

What is the slope of the line defined by the equation y = 3x - 5?

Accepted Answer

3

Answer

5

Answer

-3

Answer

-5

Question 14

Which of the following equations represents the circle with center (3, -2) and radius 5?

Accepted Answer

(x - 3)² + (y + 2)² = 25

Answer

(x - 3)² + (y + 2)² = 5

Answer

(x + 3)² + (y - 2)² = 25

Answer

(x + 3)² + (y - 2)² = 5

Question 15

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 16

The midpoint coordinates of a line segment with endpoints (a, b) and (c, d) are:

Accepted Answer

((a + c) / 2, (b + d) / 2)

Answer

((a - c) / 2, (b - d) / 2)

Answer

((a * c) / 2, (b * d) / 2)

Answer

((a + c) / 2, (b - d) / 2)

Question 17

The distance between points (x1, y1) and (x2, y2) can be calculated as:

Accepted Answer

√[(x1 - x2)² + (y1 - y2)²]

Answer

√[(x1 + x2)² + (y1 + y2)²]

Answer

√[(x1 - x2) * (y1 - y2)]

Answer

|x1 - x2| + |y1 - y2|

Question 18

The equation representing a circle with center (h, k) and radius r is:

Accepted Answer

(x - h)² + (y - k)² = r²

Answer

(x + h)² + (y + k)² = r²

Answer

(x - h) + (y - k) = r²

Answer

(x + h) + (y + k) = r²

Question 19

The graph of the inequality y > 2x - 3 corresponds to:

Accepted Answer

The region above the line y = 2x - 3

Answer

The region below the line y = 2x - 3

Answer

The line y = 2x - 3

Answer

All points in the coordinate plane

Question 20

The range of the function f(x) = |x - 1| is:

Accepted Answer

y ≥ 0

Answer

y ≤ 0

Answer

y > 0

Answer

y < 0

Question 21

Which of the following transformations will move a triangle 3 units to the left and 5 units down?

Accepted Answer

(x - 3, y - 5)

Answer

(x - 3, y + 5)

Answer

(x + 3, y + 5)

Answer

(x + 3, y - 5)

Question 22

What is the area of a rectangle with a length of 7 units and a width of 4 units?

Accepted Answer

28 square units

Answer

35 square units

Answer

11 square units

Question 23

Which of the following equations represents a horizontal line passing through the point (3, 7)?

Accepted Answer

y = 7

Answer

x = 3

Answer

x = 7

Answer

y =3

Question 24

What is the y-coordinate of the point where the line y = 4x - 3 intersects the y-axis?

Accepted Answer

-3

Answer

4

Answer

-4

Answer

3

Question 25

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

Accepted Answer

6

Answer

3

Answer

9

Question 26

Which of the following equations represents a line with a y-intercept of 4 and a slope of -3?

Accepted Answer

y = -3x + 4

Answer

y = 3x + 4

Answer

y = -3x - 4

Answer

y = 3x - 4

Question 27

What is the equation of the line that is parallel to the line y = 2x - 5 and passes through the point (1, 3)?

Accepted Answer

y = 2x + 1

Answer

y = -1/2x + 2.5

Answer

y = -1/2x + 3.5

Answer

y = 2x - 1

Question 28

What is the solution to the system of equations: 2x + y = 5 and x - y = 1?

Accepted Answer

(2, 1)

Answer

(3, -1)

Answer

(-1, 3)

Answer

(1, 2)

Question 29

The distance between the points (1, 2) and (4, 6) is:

Accepted Answer

5

Answer

7

Answer

4

Answer

3

Question 30

The midpoint of the line segment connecting the points (3, 7) and (9, 1) is:

Accepted Answer

(6, 4)

Answer

(12, 8)

Answer

(4, 6)

Answer

(3, 3)

Question 31

Which of the following points lies on the line represented by the equation y = 2x + 1?

Accepted Answer

(2, 5)

Answer

(3, 4)

Answer

(1, 3)

Answer

(0, 2)

Question 32

What is the equation of the line perpendicular to the line y = -1/3x + 2 and passing through the point (4, 1)?

Accepted Answer

y = 3x - 11

Answer

y = -3x + 13

Answer

y = -1/3x + 13/3

Answer

y = 1/3x - 1

Question 33

A system of equations has no solution if the lines represented by the equations are:

Accepted Answer

Parallel

Answer

Coincident

Answer

Perpendicular

Answer

Intersecting

Question 34

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

Accepted Answer

x = 2

Answer

y = -2x

Answer

2y = x - 3

Answer

y = 2x + 1

Question 35

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

Accepted Answer

y = -2x + 3

Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 1

Question 36

What is the distance between the points (1, 2) and (5, 7)?

Accepted Answer

√29

Answer

√32

Answer

√20

Answer

√58

Question 37

Which of the following graphs represents the equation y = 2x - 1?

Accepted Answer

[Image of a line with a slope of 2 and a y-intercept of -1]

Answer

[Image of a line with a slope of -2 and a y-intercept of 1]

Answer

[Image of a line with a slope of 1 and a y-intercept of -2]

Question 38

Which of the following transformations would translate the point (2, 3) 5 units to the right and 2 units up?

Accepted Answer

(7, 5)

Answer

(2, 5)

Answer

(2, 8)

Answer

(7, 8)

Question 39

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

Accepted Answer

2

Answer

1/2

Answer

-2

Answer

-1/2

Question 40

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

Accepted Answer

y = 3x - 2

Answer

y = 2x + 3

Answer

y = -3x - 2

Answer

y = -2x + 3

Question 41

Which of the following points lies on the line represented by the equation 2x + y = 6?

Accepted Answer

(1, 4)

Answer

(4, -2)

Answer

(3, 0)

Answer

(2, 2)

Question 42

What is the distance between the points (-1, 2) and (3, 6)?

Accepted Answer

5

Answer

2

Answer

4

Answer

3

Question 43

What is the midpoint of the line segment with endpoints (2, 5) and (8, -1)?

Accepted Answer

(5, 2)

Answer

(6, 4)

Answer

(3, 3)

Answer

(10, -6)

Question 44

Which of the following systems of equations represents the lines graphed below?

Accepted Answer

y = x + 2, y = -x + 4

Answer

y = 2x + 1, y = x - 1

Answer

y = -x + 2, y = x + 4

Answer

y = x + 1, y = -2x + 4

Question 45

What is the solution to the system of equations: x + y = 5 and x - y = 1?

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(1, 4)

Answer

(4, 1)

Question 46

A line passes through the point (2, 1) and is perpendicular to the line y = 3x - 5. What is the equation of this perpendicular line?

Accepted Answer

y = (-1/3)x + 5/3

Answer

y = (-1/3)x - 5/3

Answer

y = 3x - 5

Answer

y = 3x + 5

Question 47

A triangle has vertices at (-2, 1), (4, 1), and (4, -3). What is the area of this triangle?

Accepted Answer

12

Answer

8

Answer

24

Answer

6

Question 48

The equation of a circle is (x - 3)^2 + (y + 2)^2 = 25. What is the radius of this circle?

Accepted Answer

5

Answer

25

Answer

10