4024/22 Oct/Nov 2023, Question 7: Perpendicular Lines
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks
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The question, in short
On a centimetre grid with A(−4, 1) and B(1, 4), choose coordinates making triangle ABC isosceles, find vector AB, use A as midpoint of DB to find |DB|, and find where a perpendicular line through (6, 4) meets the x-axis.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (ai) · 2 marks
From the five listed coordinates, tick the two that make triangle ABC isosceles.
- 1AB² = 5² + 3² = 34
- 2C(−2, −1): BC² = 3² + 5² = 34 = AB², isosceles
- 3C(6, 1): BC² = 5² + 3² = 34 = AB², isosceles
- 4(−2, −1) and (6, 1)
Answer(−2, −1) and (6, 1)
Part (aii) · 1 mark
Write the column vector from A to B.
- 1→AB = (1 − (−4), 4 − 1)
- 2= column vector (5, 3)
Answercolumn vector (5, 3)
Part (aiii) · 3 marks
Given A is the midpoint of DB, find the length |DB|.
- 1A is the midpoint of DB, so →DB = 2→AB = (10, 6)
- 2|→DB| = √(10² + 6²) = √136
- 3= 11.66… ≈ 11.7
Answer11.7 or 11.66…
Part (b) · 4 marks
Line L is perpendicular to y = 4x − 3 and passes through (6, 4); find where L crosses the x-axis.
- 1Gradient of L = −1/4 (perpendicular to gradient 4)
- 24 = −1/4 × 6 + c so c = 5.5
- 3y = 0: 1/4 x = 5.5 so x = 22
- 4(22, 0)
Answer(22,0)
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Also searched as: 4024/22/O/N/23 · 4024_w23_qp_22 · 4024 w23 22 · question 7.
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