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?