Edexcel IGCSE Math A 3.3.D coordinates from geometry

Practise geometry-coordinate questions by using shape properties, parallel sides or diagonals to locate the missing labelled point.

Exam points

Find the coordinates of a point using rectangle, kite or trapezium properties.
Plot a missing point on the grid so the stated geometric condition is satisfied.

[Maximum number: 6]

25 A B C D is a trapezium with AB parallel to DC
A is the point with coordinates (-4,6)
B is the point with coordinates (2,3)
D is the point with coordinates (-1,8)
The trapezium has one line of symmetry.
The line of symmetry intersects CD at the point E
Work out the coordinates of the point E

Midpoint of AB:
$\left(\frac{-4+2}{2},\frac{6+3}{2}\right)=(-1,4.5)$
Gradient of AB:
$\frac{6-3}{-4-2}=-\frac12$
Gradient of the line of symmetry:
2
Equation of the line of symmetry through (-1,4.5):
y=2x+6.5
Equation of CD through D(-1,8), parallel to AB:
y=-0.5x+7.5
Intersection:
2x+6.5=-0.5x+7.5 $x=0.4,\qquad y=7.3$

Final answer:
(0.4,7.3)

M marks for midpoint, gradient of AB, perpendicular gradient, equations, and solving the intersection. A1 oe.

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3.3.D The coordinates of points identified by geometrical question 1