Question

when looking at the diagram below, the pre - image is figure k which is transformed somehow to figure s and then transformed to figure u. choose the correct combination of transformations.

Explanation:

Step1: Analyze transformation from K to S

Observing the position of figure K and S, we can see that figure K is translated. The x - coordinate of each point in K is decreased by 1 and the y - coordinate is decreased by 3. So the transformation from K to S is a translation $T_{(- 1,-3)}$.

Step2: Analyze transformation from S to U

Comparing figure S and U, we notice that figure S is rotated 180° about the origin. A 180 - degree rotation about the origin changes the sign of both the x - and y - coordinates of each point. The rotation is $R_{180^{\circ}}$.

Answer:

$T_{(-1,-3)}$ and then $R_{180^{\circ}}$