Coordinate Geometry Hard

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Quizzes Created: 29 | Total Attempts: 19,405
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Coordinate Geometry Hard - Quiz

Difficult coordinate geometry ACT questions


Questions and Answers
  • 1. 

    Given the vertices of parallelogram QRST in the standard (x, y) coordinate plane below, what is the area of triangle QRS, in square units?

    • A.

      24

    • B.

      28

    • C.

      48

    • D.

      60

    • E.

      80

    Correct Answer
    A. 24
    Explanation
    Area triangle = 1/2bh and the base is 6 units (from -3 to 3) and the height is 8 units (from -5 to 3). 1/2*6*8= 24 sq units

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  • 2. 

    In the standard (x, y) coordinate plane, what is the equation of the line that passes through the origin and the point (3, 4)?

    • A.

      Y = 1/4x + 3/4

    • B.

      Y = 1/4x - 1/3

    • C.

      Y = 4/3x

    • D.

      Y = 1/2x + 3/4

    • E.

      Y = 9/4x

    Correct Answer
    C. Y = 4/3x
    Explanation
    slope = 3/4. remember the origin is just the point (0, 0) so you can use the slope formula followed by point slope form: y - y1 = m(x - x1) but if you think about it, b has to be 0 if it goes through the origin!

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  • 3. 

    For what value of n would the following system of equations have an infinite number of solutions?3a + b = 1212a + 4b = 3n

    • A.

      4

    • B.

      9

    • C.

      16

    • D.

      36

    • E.

      48

    Correct Answer
    C. 16
    Explanation
    For infinite solutions, every term in the second equation would have to be a multiple of each term in the first equation. The a and b terms are clearly multiplied by 4. 12*4 = 48. So your equation is 48 = 3n, solve for n.

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  • 4. 

    What is the slope of the line that is perpendicular to the line determined by the equation 7x + 4y = 11?

    • A.

      -4

    • B.

      -7/4

    • C.

      11/4

    • D.

      4

    • E.

      4/7

    Correct Answer
    E. 4/7
    Explanation
    Solve for y - then take the opposite reciprocal of the slope since the line is perpendicular

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  • 5. 

    What is the distance in the standard (x, y) coordinate plane between points (0, 1) and (4, 4)?

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    • E.

      E

    Correct Answer
    E. E
    Explanation
    Distance formula - answer left in radical form

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  • 6. 

    In the standard (x, y) coordinate plane, if the x-coordinate of each point on a line is 5 more than half the y-coordinate, what is the slope of the line?

    • A.

      -5

    • B.

      -1/2

    • C.

      1/2

    • D.

      2

    • E.

      5

    Correct Answer
    D. 2
    Explanation
    x = 1/2y + 5. Solve for y and you get y = 2x - 5. This one is hard!

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  • 7. 

    A system of linear equations is shown below.4y = 3x + 12-4y = -3x - 8Which of the following describes the graph of this system of linear equations in the standard (x, y) coordinate plane?

    • A.

      Two parallel lines with negative slope

    • B.

      Two parallel lines with positive slope

    • C.

      A single line with negative slope

    • D.

      A single line with positive slope

    • E.

      Two perpendicular lines

    Correct Answer
    B. Two parallel lines with positive slope
    Explanation
    The solution is no solution (0 = 4) so the lines are parallel and the slope of each of them is positive 3/4 (in the second one, the two negatives cancel).

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  • 8. 

    In the standard (x, y) coordinate plane, if a square has the vertices (-2, -3), (2, -3) and (2, 1), what is the set of coordinates for the final vertex?

    • A.

      (2, -1)

    • B.

      (1, -2)

    • C.

      (-1, 2)

    • D.

      (-2, -1)

    • E.

      (-2, 1)

    Correct Answer
    E. (-2, 1)
    Explanation
    You just need to sketch this one to see it - don't try and figure it out in your head.

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  • 9. 

    Given that y - 5 = 1/2x + 1 is the equation of a line, at what point does it cross the x-axis?

    • A.

      -15

    • B.

      -12

    • C.

      1

    • D.

      4

    • E.

      6

    Correct Answer
    B. -12
    Explanation
    It crosses the x-axis when y = 0, so 0-5 = 1/2x + 1. solve for x and you should get the right answer.

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  • Current Version
  • Mar 22, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jun 23, 2010
    Quiz Created by
    Annacabral
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