Coordinate Geometry Level 1

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Coordinate Geometry ACT questions - Easy to Medium

• 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.

• B.

• C.

• D.

• E.

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)

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

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

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

C. 10.0
Explanation
Area triangle = 1/2bh and the base is 5 and the height is 4.

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