Paper 1 · Coordinate geometry

Find, in terms of $k$ , the equation of the perpendicular bisector of the line joining $A(2k, k)$ and $B(4k, 9k)$ .

4x + y = 17k

x - 4y = -17k

x + 4y = 23k

4x - y = 7k

Explanation: The midpoint is

(3k,5k)

and the gradient of

AB

4

, so the bisector has gradient

-\tfrac14

y-5k=-\tfrac14(x-3k)

, i.e.

x+4y=23k

Derived from ZIMSEC Mathematics Paper 1, June 2019, Q1

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