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: Apply translation

The translation rule $T_{- 4,2}(x,y)=(x - 4,y + 2)$. For point $W(1,6)$, we substitute $x = 1$ and $y = 6$ into the translation formula.
$(1-4,6 + 2)=(-3,8)$

Step2: Apply reflection

The reflection rule over the $y$-axis is $r_{y - axis}(x,y)=(-x,y)$. For the point $(-3,8)$ from the previous step, we substitute $x=-3$ and $y = 8$ into the reflection formula.
$(-(-3),8)=(3,8)$

Answer:

$(3,8)$