Question

multiple choice figure wxyz is transformed using a sequence of transformations. a) reflection across the y - axis b) translation (x,y)→(x - 4,y + 2) 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 y - axis reflection

The rule for reflecting a point $(x,y)$ across the $y$-axis is $(x,y)\to(-x,y)$. Given the point $W(1,6)$, after reflection across the $y$-axis, the new point $W'$ has coordinates $(- 1,6)$.

Step2: Apply translation

The translation rule is $(x,y)\to(x - 4,y + 2)$. For the point $W'(-1,6)$, we substitute $x=-1$ and $y = 6$ into the translation rule.
$x=-1-4=-5$ and $y=6 + 2=8$. So the coordinates of the final - image point $W''$ are $(-5,8)$.

Answer:

(-5,8)