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? \bigcirc (-5, 8) \bigcirc (-3, -8) \bigcirc (5, -8) \bigcirc (3, 8)

Explanation:

Step1: Apply translation first

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

Step2: Apply reflection over y-axis

The reflection rule $r_{y-axis}(x,y)$ changes the sign of the x-coordinate: $(x,y) \to (-x,y)$.
For the translated point $(-3, 8)$:
$x'' = -(-3) = 3$
$y'' = 8$
Result after reflection: $(3, 8)$

Answer:

D. (3, 8)