Coordinate Geometry Level 1

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Coordinate Geometry Level 1 - Quiz


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.

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