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Coordinate Geometry ACT questions - Easy to Medium
Questions and Answers
1.
Point A is to be graphed in a quadrant, not on an axis, of the standard (x, y) coordinate plane below. If the x-coordinate and the y-coordinate of point A are to have the same signs, then point A must be located in:
A.
Quadrant I only
B.
Quadrant II only
C.
Quadrant III only
D.
Quadrant I or II only
E.
Quadrant I or III only
Correct Answer E. Quadrant I or III only
Explanation If the x-coordinate and the y-coordinate of point A are to have the same signs, it means that both coordinates will either be positive or negative. In Quadrant I, both x and y coordinates are positive, while in Quadrant III, both x and y coordinates are negative. Therefore, point A must be located in either Quadrant I or III only to satisfy the given condition.
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2.
In the standard (x, y) coordinate plane, point X has coordinates (-4, 0) and point Y has coordinates (0, -8). What are the coordinates of the midpoint of XY?
A.
(-6, -1)
B.
(-2, -4)
C.
(0, 2)
D.
(2, 4)
E.
(6, -1)
Correct Answer B. (-2, -4)
Explanation The midpoint of a line segment is the point that is exactly halfway between the two endpoints. To find the coordinates of the midpoint, we average the x-coordinates and the y-coordinates of the endpoints separately. In this case, the x-coordinate of the midpoint is (-4 + 0)/2 = -2, and the y-coordinate is (0 + (-8))/2 = -4. Therefore, the coordinates of the midpoint of XY are (-2, -4).
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3.
In the standard (x, y) coordinate plane, what is the slope of the line joining the points (3, 7) and (4, -8)?
A.
-15
B.
-1
C.
-1/7
D.
21/32
E.
15
Correct Answer A. -15
Explanation The slope of a line is determined by the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, the change in y is -8 - 7 = -15 and the change in x is 4 - 3 = 1. Therefore, the slope is -15/1 = -15.
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4.
What is the slope of the line that passes through the origin and the point (-6, 2)?
A.
3
B.
1/3
C.
-1/3
D.
-3
E.
-6
Correct Answer C. -1/3
Explanation Remember the origin is the point (0, 0) and slope = (y2-y1)/(x2-x1)
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5.
What is the area, in coordinate units, of the triangle in the figure below?
A.
4.5
B.
9.0
C.
10.0
D.
12.5
E.
20.0
Correct Answer C. 10.0
Explanation Area triangle = 1/2bh and the base is 5 and the height is 4.