Coordinate Geometry Act Questions

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Coordinate Geometry Act Questions - Quiz

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. 32
    Explanation
    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.

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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. 12.81
    Explanation
    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.

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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. 22
    Explanation
    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.

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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. 5
    Explanation
    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.

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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. 8/5
    Explanation
    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.

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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. 5
    Explanation
    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.

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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. 1/6
    Explanation
    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.

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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).

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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. 1
    Explanation
    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.

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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. 2/5
    Explanation
    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.

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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 - 8
    Explanation
    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.

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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. B
    Explanation
    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.

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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. 2/3
    Explanation
    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.

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