Higher November 2023 Paper 1 Q18

(a) \(P\) and \(Q\) are points.

\(P\,(-3, -2)\) is mapped to \(Q\) by a rotation about \((1, 0)\) through 90° clockwise.

\(Q\) is mapped back to \(P\) by a single transformation.

Complete these two single transformations that each map \(Q\) back to \(P\). [2 marks]

Rotation about \((1, 0)\) ____________
Translation ____________

(b) Point \(A\,(7, 4)\) and the line \(\quad y = x \quad\) are shown on the grid.

\(B\) and \(C\) are points on the grid, each having positive integer coordinates.

\(BAC\) is a right-angled triangle.
When \(BAC\) is reflected in the line \(\quad y = x \quad\) side \(BC\) is invariant.

Work out one possible set of coordinates for \(B\) and \(C\). [1 mark]