Parallel and Perpendicular Lines in Coordinates · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Parallel and Perpendicular Lines in Coordinates

Mathematics · Geometry · ages 16-17
Name ______________________   Date ____________

  1. What is the distance between the points (1, 2) and (4, 6)?

    Answer: ______________

  2. A line is parallel to 2x + y - 5 = 0. What is its gradient?

    • -2
    • 2
    • -1/2
    • 1/2

  3. Which slope is perpendicular to a line with slope -4?

    • -4
    • 0.25
    • 4
    • -0.25

  4. The lines y = 3x + 5 and y = 3x - 2 are parallel.

    Circle one:   True   False

  5. What is the distance between the points (-2, 3) and (3, 15)?

    Answer: ______________

  6. The line 3x + y - 4 = 0 is perpendicular to the line y = (1/3)x + 2.

    Circle one:   True   False

  7. A point sits on the perpendicular bisector of AB and is 12 units from A. It is therefore 12 units from B.

    Circle one:   True   False

  8. A line through (3, 1) is parallel to y = -4x + 9. Where does it cross the y-axis?

    Answer: ______________

  9. A triangle has vertices P(0, 0), Q(4, 2) and R(2, 6). Which angle is a right angle?

    • the angle at P
    • the angle at R
    • the angle at Q
    • none of them is a right angle

  10. Find the equation of the perpendicular bisector of the segment joining (2, 3) and (8, 7).

    • y = -1.5x + 12.5
    • y = 1.5x - 2.5
    • y = -0.667x + 8.33
    • y = 0.667x + 1.67
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Answer key

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Parallel and Perpendicular Lines in Coordinates W1-mt_xNEmm139Ka-s1

  1. 5 · The horizontal gap is 4 - 1 = 3 and the vertical gap is 6 - 2 = 4. The distance is the square root of 3² + 4², which is the square root of 25, so 5.
  2. -2 · Rearranging gives y = -2x + 5, so the gradient is -2. A parallel line has the same gradient.
  3. 0.25 · Perpendicular slopes are negative reciprocals of each other.
  4. True · Same slope, different intercept means the lines run side by side forever.
  5. 13 · The gaps are 3 - (-2) = 5 and 15 - 3 = 12. The distance is the square root of 5² + 12², which is the square root of 169, so 13.
  6. True · Rearranging the first gives y = -3x + 4, so its gradient is -3. Then -3 times 1/3 is -1, so the lines are perpendicular.
  7. True · The bisector is exactly the set of points that are equally far from both ends, so a distance of 12 to A forces a distance of 12 to B.
  8. 13 · Parallel means the same gradient, so y = -4x + c. Putting in (3, 1) gives 1 = -12 + c, so c = 13.
  9. the angle at Q · PQ has gradient 1/2 and QR has gradient -2, and 1/2 times -2 is -1. Those two sides meet at Q, so the right angle is at Q.
  10. y = -1.5x + 12.5 · The bisector passes through the midpoint at a right angle to the original segment.
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