O-LevelMathematicsVectors and transformations4024/21 · Oct/Nov 2020 · Q912 Marks

H is the point (5, 2) and J is the point (-3, 6). Find HJ.

(a)(i)H is the point (5, 2) and J is the point (-3, 6). Find HJ.[1]
(a)(ii)Calculate the magnitude of HJ.[2]
(a)(iii)M is the midpoint of HJ. Find the position vector of M.[2]
(b)(i)(a)The diagram shows a shape made from seven identical equilateral triangles. OÀ = p and OF = q. Express, as simply as possible, in terms of p and/or q FB,[1]
(b)(i)(b)FÊ.[1]
(b)(ii)X is a point on FB and FX : XB = 3 : 1. Express OX, as simply as possible, in terms of p and/or q.[2]
(b)(iii)Y is a point on BD. Quadrilateral OXYF is a trapezium. Express XÝ, as simply as possible, in terms of p and/or q.[3]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[1] (-8, 4)
[2] 8.94[4...] nfww M1 for (their−8)² +(their 4)² oe
[2] (1, 4) B1 for one component correct or for (1, 4) seen or B1FT for (4, 2)
[1] 2p
[1] p + q
[2] 3/2 p + q oe simplified vector final answer B1 for FX = 3/2 p soi or BX = 1/2 p soi or M1 for a correct vector route along the lines of the diagram
[3] 1/2 p + 3/4 q oe simplified vector final answer B2 for answer kp + 3/4 q or 1/2 p + kq or correct unsimplified vector or for FY = 2p + 3/4 q oe or M1 for FY = kOX soi or for correct route for XY

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