Question

1. explain by using mappings how square a has been translated to square a?

Explanation:

Step1: Identify the horizontal translation

For a point \((x,y)\) in square \(A\), observe the change in the \(x -\)coordinate. If we take a vertex of square \(A\) (say \((x_1,y_1)\)) and the corresponding vertex of square \(A'\) (say \((x_2,y_2)\)). The horizontal translation (change in \(x\)): assume \(x_1\) and \(x_2\). If \(x_1 - x_2=0\) (no horizontal shift).

Step2: Identify the vertical translation

The vertical translation (change in \(y\)): If we take a vertex of square \(A\) (say \((x,y_1)\)) and the corresponding vertex of square \(A'\) (say \((x,y_2)\)). We can see that for each point \((x,y)\) in square \(A\), the mapping to square \(A'\) is \((x,y)\to(x,y - 3)\) (by counting the number of units between a corresponding pair of vertices in the vertical direction).

Answer:

The translation mapping is \((x,y)\to(x,y - 3)\)