Question

determining coordinates after a sequence of transformations
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?
$(1, - 2)$ $(5, - 6)$ $(5,6)$ $(1,2)$

Explanation:

Step1: Perform translation

The translation $T_{2,2}$ means moving the point 2 units to the right and 2 units up. If the original point $B$ has coordinates $(3,4)$, after translation, the $x$-coordinate becomes $3 + 2=5$ and the $y$-coordinate becomes $4 + 2 = 6$. So the coordinates of the point after translation are $(5,6)$.

Step2: Perform reflection

The reflection $r_{x - axis}$ changes the sign of the $y$-coordinate. For the point $(5,6)$ after reflection across the $x$-axis, the $x$-coordinate remains $5$ and the $y$-coordinate becomes $- 6$. So the final - image point $B''$ has coordinates $(5,-6)$.

Answer:

$(5,-6)$