WMA11/01 Jun 2021, Question 7: Perpendicular Lines
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks
The question, in short
For line l₁ with equation 4y + 3x = 48 and point D(8, 6), find the y-intercept C, the y-intercept E of the perpendicular line l₂, the arc length BE of a 1.8 radian sector, and the area of region CBED.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 1 mark
State the y coordinate of point C where l₁ crosses the y-axis.
- 1At x = 0: 4y = 48
- 2y = 12
Answer12
Part (b) · 3 marks
Show that the y coordinate of E, where the perpendicular line l₂ through D meets the y-axis, is −14/3.
- 1l₁: y = 12 − (3/4)x, so gradient of l₁ = −3/4
- 2Gradient of l₂ = 4/3
- 3l₂: y − 6 = (4/3)(x − 8)
- 4At x = 0: y = 6 − 32/3 = −14/3
AnswerShown: l₂: y − 6 = (4/3)(x − 8); at x = 0, y = 6 − 32/3 = −14/3
Part (c) · 3 marks
Given angle BCE is 1.8 radians, find the length of arc BE of the sector centred at C.
- 1Radius CE = 12 − (−14/3) = 50/3
- 2Arc BE = rθ = (50/3) × 1.8
- 3= 30
Answer30
Part (d) · 3 marks
Calculate the exact area of the shaded region CBED, made from sector BCE joined to triangle CDE.
- 1Sector area = ½r²θ = ½ × (50/3)² × 1.8 = 250
- 2Triangle CDE: base CE = 50/3 on the y-axis, height = x-coordinate of D = 8
- 3Triangle area = ½ × (50/3) × 8 = 200/3
- 4Total = 250 + 200/3 = 950/3
Answer950/3
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