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 $W(1,6)$, after translation, we have $x_1=1-4=-3$ and $y_1=6 + 2=8$, so the point becomes $(-3,8)$.

Step2: Apply reflection

The reflection rule over the $y$-axis is $r_{y - axis}(x,y)=(-x,y)$. For the point $(-3,8)$ after reflection over the $y$-axis, we get $x_2=-(-3)=3$ and $y_2 = 8$. So the final - point $W''$ is $(3,8)$.

Answer:

$(3,8)$