Question

given the transformation below of abcde to its image abcde, which of the following rules expresses the transformation? f(x,y)→f(−y,−x) f(x,y)→f(−y,x) f(x,y)→f(−x,−y) f(x,y)→f(x,−y)

Explanation:

Step1: Observe coordinate - change pattern

Pick a point, say \(A\). Let's assume the coordinates of \(A\) are \((x_1,y_1)\) and the coordinates of \(A'\) are \((x_2,y_2)\). By looking at the graph, we can see that if we have a point \((x,y)\) in the original figure, its image has coordinates \((-x,-y)\). For example, if a point is in the first - quadrant \((x,y)\) (\(x>0,y > 0\)), its image is in the third - quadrant \((-x,-y)\) (\(-x<0,-y < 0\)).

Step2: Match with transformation rules

We check each option. The rule \(f(x,y)\to f(-x,-y)\) is a rotation of \(180^{\circ}\) about the origin. This rule correctly maps the points of \(ABCDE\) to \(A'B'C'D'E'\).

Answer:

\(f(x,y)\to f(-x,-y)\)