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 transformation

The transformation $T_{2,2}$ is a translation. For a point $(x,y)$, the translation $T_{2,2}$ changes the coordinates as $(x,y)\to(x + 2,y+2)$. Given the point $B(3,4)$, after the translation $T_{2,2}$, the new - point $B'$ has coordinates $(3 + 2,4 + 2)=(5,6)$.

Step2: Apply reflection transformation

The transformation $r_{x - axis}$ is a reflection over the $x$-axis. The rule for reflecting a point $(x,y)$ over the $x$-axis is $(x,y)\to(x,-y)$. For the point $B'(5,6)$, after the reflection $r_{x - axis}$, the new - point $B''$ has coordinates $(5,-6)$.

Answer:

B. $(5,-6)$