Review question

# Can we show we have three corners of a rectangle? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5386

## Suggestion

The coordinates of the points $A$, $B$, $C$ are $(-2,1)$, $(2,7)$, $(5,5)$ respectively. Prove that these points form three corners of a rectangle…

Can we find the gradients of two sides of the rectangle?

What do we know about adjacent sides of a rectangle (or the angle between them)?

…and that $AB=2BC$.

Can similar triangles help us here? Or can we use the formula for the distance between two points?

If $D$ is the fourth corner of the rectangle, calculate the distance of $C$ from the diagonal $BD$.

There are often multiple ways to calculate the distance of a point from a line.

Recall that the shortest distance is given by dropping a perpendicular from the point $C$ onto the line $BD$.

If we draw a diagram, could we use similar triangles again?