# Coordinate Geometry Hard

9 Questions | Total Attempts: 967  Settings  Difficult coordinate geometry ACT questions

• 1.
Given the vertices of parallelogram QRST in the standard (x, y) coordinate plane below, what is the area of triangle QRS, in square units?
• A.

24

• B.

28

• C.

48

• D.

60

• E.

80

• 2.
In the standard (x, y) coordinate plane, what is the equation of the line that passes through the origin and the point (3, 4)?
• A.

Y = 1/4x + 3/4

• B.

Y = 1/4x - 1/3

• C.

Y = 4/3x

• D.

Y = 1/2x + 3/4

• E.

Y = 9/4x

• 3.
For what value of n would the following system of equations have an infinite number of solutions?3a + b = 1212a + 4b = 3n
• A.

4

• B.

9

• C.

16

• D.

36

• E.

48

• 4.
What is the slope of the line that is perpendicular to the line determined by the equation 7x + 4y = 11?
• A.

-4

• B.

-7/4

• C.

11/4

• D.

4

• E.

4/7

• 5.
What is the distance in the standard (x, y) coordinate plane between points (0, 1) and (4, 4)?
• A.

A

• B.

B

• C.

C

• D.

D

• E.

E

• 6.
In the standard (x, y) coordinate plane, if the x-coordinate of each point on a line is 5 more than half the y-coordinate, what is the slope of the line?
• A.

-5

• B.

-1/2

• C.

1/2

• D.

2

• E.

5

• 7.
A system of linear equations is shown below.4y = 3x + 12-4y = -3x - 8Which of the following describes the graph of this system of linear equations in the standard (x, y) coordinate plane?
• A.

Two parallel lines with negative slope

• B.

Two parallel lines with positive slope

• C.

A single line with negative slope

• D.

A single line with positive slope

• E.

Two perpendicular lines

• 8.
In the standard (x, y) coordinate plane, if a square has the vertices (-2, -3), (2, -3) and (2, 1), what is the set of coordinates for the final vertex?
• A.

(2, -1)

• B.

(1, -2)

• C.

(-1, 2)

• D.

(-2, -1)

• E.

(-2, 1)

• 9.
Given that y - 5 = 1/2x + 1 is the equation of a line, at what point does it cross the x-axis?
• A.

-15

• B.

-12

• C.

1

• D.

4

• E.

6

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