22M.1.SL.TZ1.1

pestleMathematicsAASLPaper 122M· sl-2-1-equations-of-straight-lines-parallel-and-perpendicularsource ↗

Consider the points $A (- 2, 20)$ , $B (4, 6)$ and $C (- 14, 12)$ . The line $L$ passes through the point $A$ and is perpendicular to $[BC]$ .

Find the equation of $L$ .

[3]

The line $L$ passes through the point $(k, 2)$ .

Find the value of $k$ .

[2]

Markscheme / solution

$m_{BC} = \frac{12 - 6}{- 14 - 4} (= - \frac{1}{3})$ (A1)

finding $m_{L} = \frac{- 1}{m_{BC}}$ using their $m_{BC}$ (M1)

$m_{L} = 3$

$y - 20 = 3 (x + 2), y = 3 x + 26$ A1

Note: Do not accept $L = 3 x + 26$

[3 marks]

substituting $(k, 2)$ into their $L$ (M1)

$2 - 20 = 3 (k + 2)$ OR $2 = 3 k + 26$

$k = - 8$ A1

[2 marks]

Examiners’ report

Finding the gradient of a line was well understood and many candidates also correctly found the perpendicular slope. Even with an error in their part (a), follow through marks in part (b) allowed many candidates to earn full marks for finding k despite their incorrect equation resulting in arithmetic of greater complexity.

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