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 $T_{2,2}$

The rule for the translation $T_{2,2}$ is $(x,y)\to(x + 2,y + 2)$. Given the point $B(3,4)$, after the translation, we have $(3+2,4 + 2)=(5,6)$.

Step2: Apply reflection $r_{x - axis}$

The rule for reflection over the $x$-axis is $(x,y)\to(x,-y)$. For the point $(5,6)$ after reflection over the $x$-axis, we get $(5,-6)$.

Answer:

$(5,-6)$