Question

figure bcde was transformed using the composition $r_{x - axis}circ t_{2,2}$. if point b on the pre - image lies at (3, 4), what are the coordinates of b on the final image? (5, 6) (5, - 6) (1, 2) (1, - 2)

Explanation:

Step1: Apply translation $T_{2,2}$

For a translation $T_{2,2}$, we add 2 to the $x$-coordinate and 2 to the $y$-coordinate of the point. Given the point $B(3,4)$, after translation, the coordinates become $(3 + 2,4+ 2)=(5,6)$.

Step2: Apply reflection over $x$-axis

The rule for reflecting a point $(x,y)$ over the $x$-axis is $(x,-y)$. For the point $(5,6)$ after reflection over the $x$-axis, the coordinates become $(5,-6)$.

Answer:

B. $(5,-6)$