Edexcel IGCSE Math B 6.D Quadrilaterals Question Bank

Practise using quadrilateral properties with coordinates or vectors, especially when a named shape fixes a missing vertex.

Exam points

use kite properties with coordinates or vectors to find a missing point

[Maximum number: 3]

Figure for Question 6.D Quadrilaterals question 1 — Edexcel IGCSE Math B

Diagram NOT accurately drawn.

Figure 2 shows a quadrilateral ABCD with
$\overrightarrow{AB}=\binom{8.5}{4.5}\quad\text{and}\quad \overrightarrow{AC}=\binom{15}{5}.$
The diagonals AC and BD meet at the point E.

Given that ABCD is a kite, find the coordinates of the point D.

$\overrightarrow{OB}=\binom{-3}{1}+\binom{8.5}{4.5}=\binom{5.5}{5.5}$ $\overrightarrow{BE}=\binom{-8.5}{-4.5}+\binom{3}{-1}+\binom{6}{4}=\binom{0.5}{-1.5}$ $\overrightarrow{OD}=\overrightarrow{OE}+\overrightarrow{BE} =\binom{6}{4}+\binom{0.5}{-1.5} =\binom{6.5}{2.5}$

Final answer:
(6.5,2.5)

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6.D Quadrilaterals question 1