Coordinate Geometry Act Questions
Coordinate Geometry ACT Questions
Questions and Answers
- 1.
In the standard (x,y) coordinate plane below, the points (0,2), (8,2), (3,6) and (11,6) are teh vertices of a parallelogram. What ist he area, in square units, of the parallelogram?
- A.
8.49
- B.
16
- C.
32
- D.
56
- E.
88
Correct Answer
C. 32Explanation
The given points form a parallelogram in the coordinate plane. To find the area of a parallelogram, we can use the formula: base x height. The base of the parallelogram is the distance between the points (0,2) and (8,2), which is 8 units. The height of the parallelogram is the distance between the points (0,2) and (3,6), which is 4 units. Therefore, the area of the parallelogram is 8 x 4 = 32 square units.Rate this question:
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- 2.
What is the approximate distance between the points (4, -3) and (-6, 5) in the standard (x, y) coordinate plane?
- A.
8.92
- B.
12.81
- C.
16.97
- D.
17.95
- E.
19.22
Correct Answer
B. 12.81Explanation
The approximate distance between two points in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the two points are (4, -3) and (-6, 5). Plugging these values into the distance formula, we get:
d = √((-6 - 4)^2 + (5 - (-3))^2)
= √((-10)^2 + (8)^2)
= √(100 + 64)
= √(164)
≈ 12.81
Therefore, the approximate distance between the two points is 12.81.Rate this question:
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- 3.
Given the vertices of parallelogram FGHJ in the standard (x, y) coordinate plane below, what is the area of triangle GHJ in square units?
- A.
11
- B.
15
- C.
22
- D.
44
- E.
88
Correct Answer
C. 22Explanation
To find the area of triangle GHJ, we need to calculate the base and height of the triangle. The base is the distance between points G and H, which can be found using the distance formula. The height is the distance between the line containing points G and H and point J, which can be found by calculating the perpendicular distance from point J to the line containing points G and H. Once we have the base and height, we can use the formula for the area of a triangle (1/2 * base * height) to find the area.Rate this question:
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- 4.
In the figure above, OS = ST and the coordinates of T are (k, 5). What is the value of k?
- A.
-5
- B.
-3
- C.
-2
- D.
0
- E.
5
Correct Answer
E. 5Explanation
In the figure, it is given that OS = ST, which means that the length of OS is equal to the length of ST. The coordinates of T are given as (k, 5). Since OS = ST, the y-coordinate of T should also be 5. Therefore, the value of k should be such that the point T has a y-coordinate of 5. Looking at the answer options, the only value that satisfies this condition is k = 5.Rate this question:
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- 5.
What is the slope of a line that is perpendicular to the line determined by the equation 5x + 8y = 17?
- A.
-3
- B.
-5/8
- C.
17/8
- D.
3/17
- E.
8/5
Correct Answer
E. 8/5Explanation
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The given equation can be rewritten in slope-intercept form as y = (-5/8)x + 17/8. Therefore, the slope of the original line is -5/8. The negative reciprocal of -5/8 is 8/5, which is the slope of the line perpendicular to the given line.Rate this question:
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- 6.
In the standard (x, y) coordinate plane shown below, what is the distance on the y-axis, in units, from point A to point B?
- A.
-3
- B.
-5
- C.
3
- D.
5
- E.
11
Correct Answer
D. 5Explanation
The distance on the y-axis from point A to point B is 5 units. This can be determined by subtracting the y-coordinate of point A from the y-coordinate of point B, which gives a difference of 5.Rate this question:
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- 7.
An overlay of an accessibility ramp of a building is placed on the standard (x,y) coordinate plane so that the x-axis aligns with the horizontal. The line segment representing the side view of the ramp goes through the point (-2, -1) and (16, 2). What is the slope of the accessibility ramp?
- A.
-3
- B.
-1/3
- C.
-1/6
- D.
1/6
- E.
1/14
Correct Answer
D. 1/6Explanation
The slope of a line can be found by calculating the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the change in y-coordinates is 2 - (-1) = 3, and the change in x-coordinates is 16 - (-2) = 18. Therefore, the slope of the accessibility ramp is 3/18, which simplifies to 1/6.Rate this question:
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- 8.
In the standard (x, y) coordinate plane, point B with coordinates (5, 6) is the midpoint of AC, and A has coordinates (6, 7). What are the coordinates of C?
- A.
(11, 13)
- B.
(7, 8)
- C.
(4, 5)
- D.
(5.5, 6.5)
- E.
(-4, -8)
Correct Answer
C. (4, 5)Explanation
Since point B is the midpoint of AC, the coordinates of point C can be found by using the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. In this case, the x-coordinate of point C is (6 + x) / 2 = 5, which gives x = 4. Similarly, the y-coordinate of point C is (7 + y) / 2 = 6, which gives y = 5. Therefore, the coordinates of point C are (4, 5).Rate this question:
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- 9.
In the square graphed below, what is the slope of the line segment AC?
- A.
4
- B.
2
- C.
1
- D.
-1
- E.
-4
Correct Answer
C. 1Explanation
The slope of a line segment can be determined by finding the change in the y-coordinates divided by the change in the x-coordinates. In this case, the line segment AC goes from point A to point C, which has a change in y-coordinate of 2 and a change in x-coordinate of 2. Therefore, the slope of the line segment AC is 2/2 = 1.Rate this question:
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- 10.
Which of the following is the slope of a line parallel to the line y = 2/5x + 7 in the standard (x, y) plane?
- A.
-7
- B.
-5/2
- C.
2/5
- D.
2
- E.
5/2
Correct Answer
C. 2/5Explanation
The slope of a line parallel to another line will have the same slope. In this case, the given line has a slope of 2/5. Therefore, the slope of a line parallel to it will also be 2/5.Rate this question:
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- 11.
Quadrilateral QRST is shown below in the standard (x, y) coordinate plane.What is the length of QS in coordinate units?
- A.
A
- B.
B
- C.
C
- D.
D
- E.
E
Correct Answer
A. A -
- 12.
Which of the following is closest to the perimeter of quadrilateral QRST, in coordinate units?
- A.
26.0
- B.
22.5
- C.
19.8
- D.
15.0
- E.
14.0
Correct Answer
C. 19.8 -
- 13.
What is the slope-intercept form of 10x - y - 8 = 0?
- A.
Y = -2x
- B.
Y = -10x - 8
- C.
Y = -10x + 8
- D.
Y = 10x - 8
- E.
Y = 10x + 8
Correct Answer
D. Y = 10x - 8Explanation
The given equation is in the form of Ax + By + C = 0. To convert it to slope-intercept form (y = mx + b), we need to isolate y. By rearranging the equation, we get y = 10x - 8. Therefore, the correct answer is y = 10x - 8.Rate this question:
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- 14.
What is the distance in standard (x, y) coordinate plane between the points (5, 5) and (1, 0)?
- A.
A
- B.
B
- C.
C
- D.
D
- E.
E
Correct Answer
B. BExplanation
The distance between two points in a standard (x, y) coordinate plane can be calculated using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates of the two points. In this case, the x-coordinate difference is 5-1=4 and the y-coordinate difference is 5-0=5. Therefore, the distance is the square root of (4^2 + 5^2) = square root of (16 + 25) = square root of 41.Rate this question:
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- 15.
What is the slope of the line determined by the equation 2x - 3y = 6?
- A.
-6
- B.
-3
- C.
-3/2
- D.
2/3
- E.
2
Correct Answer
D. 2/3Explanation
The slope of a line can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m represents the slope. In this case, rearranging 2x - 3y = 6 gives -3y = -2x + 6, then dividing by -3 yields y = (2/3)x - 2. Therefore, the slope of the line is 2/3.Rate this question:
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Mar 19, 2023Quiz Edited by
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May 19, 2010Quiz Created by
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