Question

figure wxyz is transformed using the rule $r_{y - axis} circ t_{-4,2}(x,y)$. point w of the pre - image is at (1,6). what are the coordinates of point w on the final image? (-5,8) (-3,-8) (5,-8) (3,8)

Explanation:

Step1: Analyze the translation part

The translation rule $T_{- 4,2}(x,y)$ means we subtract 4 from the $x$-coordinate and add 2 to the $y$-coordinate of the point. For point $W(1,6)$, after translation: $x_1=1 - 4=-3$, $y_1=6 + 2 = 8$. So the point after translation is $(-3,8)$.

Step2: Analyze the reflection part

The reflection rule $r_{y - axis}(x,y)=(-x,y)$. Applying this to the point $(-3,8)$ after translation, we change the sign of the $x$-coordinate. So $x_2=-(-3)=3$, $y_2 = 8$.

Answer:

D. $(3,8)$