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TMUA 2017 · Paper 1 · Question 3 of 20

TMUA 2017 Paper 1 Question 3

Coordinate geometry — Perpendicular lines · area of an enclosed triangle. Try it first; the answer and a full worked solution are below.

TMUA 2017 · Paper 1Coordinate geometryPerpendicular lines · area of an enclosed triangle5 options
A line l has equation y = 6 − 2x.

A second line is perpendicular to l and passes through the point (−6,  0).

Find the area of the region enclosed by the two lines and the x-axis.

  1. A1615
  2. B18
  3. C2135
  4. D27
  5. E4012
Show the answer and worked solution
answer · A
  1. A1615
  2. B18
  3. C2135
  4. D27
  5. E4012
The perpendicular has gradient 12, so through (−6, 0) it is y = 12(x+6). The two lines cut the x-axis at x = 3 and x = −6, so that side of the triangle has length 9. They meet where 6 − 2x = 12(x+6), giving 12 − 4x = x + 6, so x = 65 and y = 185. That y-value is the height, so the area is 12 × 9 × 185 = 815 = 1615.