\(P\) is the point of intersection of the lines \(y+x=1\) and \(3y+2x=1\). Find the co-ordinates of the point midway between \(P\) and the line \(y=2x+8\).

Have you drawn a diagram yet? If you’re not sure where to start, sketch the three lines.

What is the gradient of a line perpendicular to \(y=2x+8\)? Can you find the equation of the one such line through \(P\)?