Coordinate Geometry Hard
Difficult coordinate geometry ACT questions
Questions and Answers
- 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
Correct Answer
A. 24Explanation
Area triangle = 1/2bh and the base is 6 units (from -3 to 3) and the height is 8 units (from -5 to 3). 1/2*6*8= 24 sq unitsRate this question:
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- 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
Correct Answer
C. Y = 4/3xExplanation
slope = 3/4. remember the origin is just the point (0, 0) so you can use the slope formula followed by point slope form: y - y1 = m(x - x1) but if you think about it, b has to be 0 if it goes through the origin!Rate this question:
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- 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
Correct Answer
C. 16Explanation
For infinite solutions, every term in the second equation would have to be a multiple of each term in the first equation. The a and b terms are clearly multiplied by 4. 12*4 = 48. So your equation is 48 = 3n, solve for n.Rate this question:
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- 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
Correct Answer
E. 4/7Explanation
Solve for y - then take the opposite reciprocal of the slope since the line is perpendicularRate this question:
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- 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
Correct Answer
E. EExplanation
Distance formula - answer left in radical formRate this question:
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- 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
Correct Answer
D. 2Explanation
x = 1/2y + 5. Solve for y and you get y = 2x - 5. This one is hard!Rate this question:
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- 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
Correct Answer
B. Two parallel lines with positive slopeExplanation
The solution is no solution (0 = 4) so the lines are parallel and the slope of each of them is positive 3/4 (in the second one, the two negatives cancel).Rate this question:
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- 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)
Correct Answer
E. (-2, 1)Explanation
You just need to sketch this one to see it - don't try and figure it out in your head.Rate this question:
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- 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
Correct Answer
B. -12Explanation
It crosses the x-axis when y = 0, so 0-5 = 1/2x + 1. solve for x and you should get the right answer.Rate this question:
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Mar 22, 2023Quiz Edited by
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Jun 23, 2010Quiz Created by
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