Solving Geometry Problems on Axes
# Solving Geometry Problems on Axes

GCSE(F),

Problems involving coordinates on axes need to be related to the `(x, y)` coordinates of the axes.
Draw or plot any given lines or coordinates. Answers should be given as coordinates (unless otherwise specified).

## Examples

1. Three congruent triangles are shown below. What are the coordinates of point D?

Answer: (3, 4)

The triangles are congruent and are therefore all the same size.

The height of two triangles is given by the *y*-coordinate of B minus the *y*-coordinate of A

7 - 1 = 6

The height of one triangle = 6 รท 2 = 3

Point D is immediately above point A, so the *x*-coordinate is unchanged.

Point D = (3, 1 + 3) = (3, 4)

2. A triangle has a right angle at point A. the triangle is reflected in the line `x=y`. What are the coordinates of point B?

Answer: (3, 5)

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