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. The lines y = 5x - 1 and y = 5x + 6 meet at exactly one point.

    Circle one:   True   False

  2. Two lines with the same gradient and the same y-intercept are parallel.

    Circle one:   True   False

  3. Which pair of gradients belongs to two perpendicular lines?

    • 2 and 1/2
    • 2 and -2
    • -2 and -1/2
    • 2 and -1/2

  4. A line has gradient 4. What is the gradient of any line perpendicular to it?

    • 4
    • -1/4
    • -4
    • 1/4

  5. Find the line through (2, 3) that is perpendicular to y = 4x + 1.

    • x - 4y + 14 = 0
    • x + 4y - 14 = 0
    • 4x + y - 11 = 0
    • x + 4y - 10 = 0

  6. 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

  7. A line has gradient -2/5. What is the gradient of a line perpendicular to it?

    • -5/2
    • 2/5
    • 5/2
    • -2/5

  8. Nadia says y = 5x + 1 and y = -5x + 4 are perpendicular because the gradients have opposite signs. Where is the slip?

    • the two lines are parallel, because 5 and -5 are the same size
    • she should have compared the intercepts instead of the gradients
    • the gradients should have been added, not compared
    • the test is a product of -1, and 5 times -5 is -25

  9. A line perpendicular to y = (1/2)x + 4 passes through (6, 5). Where does it cross the y-axis?

    Answer: ______________

  10. Raj finds the midpoint of (2, 9) and (8, 3) by subtracting each pair and halving, and gets (3, 3). Where is the slip?

    • he should have halved before subtracting
    • the midpoint of these two points cannot be found this way round
    • a midpoint averages, so it adds and halves, giving (5, 6)
    • he swapped the two coordinates at the end
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Parallel and Perpendicular Lines in Coordinates W1-mt_xNEmm139Ka-s1

  1. False · Both have gradient 5 and their intercepts differ, so they are parallel and never meet. There is no point on both of them.
  2. False · If both the gradient and the intercept match, the two equations describe one line, not a parallel pair. Parallel lines never meet, and a line meets itself everywhere.
  3. 2 and -1/2 · Multiply each pair and look for -1. Only 2 times -1/2 gives -1. The others give 1, -4 and 1.
  4. -1/4 · The two gradients must multiply to -1. Since 4 times -1/4 is -1, the perpendicular gradient is -1/4.
  5. x + 4y - 14 = 0 · The perpendicular gradient is -1/4. From y - 3 = -(1/4)(x - 2), multiplying by 4 gives 4y - 12 = -x + 2, which tidies to x + 4y - 14 = 0.
  6. 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.
  7. 5/2 · Flip the fraction to -5/2, then change the sign to 5/2. Check: -2/5 times 5/2 is -1.
  8. the test is a product of -1, and 5 times -5 is -25 · Opposite signs are not the test. The gradients must multiply to -1, and 5 times -5 is -25, so these lines cross at an angle that is not a right angle.
  9. 17 · The perpendicular gradient is -2. From y - 5 = -2(x - 6) you get y = -2x + 12 + 5, so y = -2x + 17 and the crossing is at 17.
  10. a midpoint averages, so it adds and halves, giving (5, 6) · Subtracting and halving gives the size of the gap, not a position. Averaging gives (2 + 8) / 2 = 5 and (9 + 3) / 2 = 6, so the midpoint is (5, 6).
Worksheet · LightMySky