A-level · Coordinate geometry

Length and midpoint of a line segmentExam-style questions

The distance between two points as Pythagoras on the horizontal and vertical gaps (left in exact surd form), and the midpoint as the average of the coordinates — plus working backwards from a known midpoint.

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2 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

1
The distance between $P(1, a)$ and $Q(5, 2)$ is $\sqrt{20}$ . Find the possible values of $a$ .
Level 3 · 3 marksTry it
2
The triangle has vertices $A(-1, 2)$ , $B(3, 4)$ and $C(5, 0)$ . Show that it is isosceles.
Level 3 · 3 marksTry it