Question

a sequence of transformations is performed on △abc, resulting in △abc. both triangles are shown on the coordinate plane below. some transformations are listed below. • (r_x): a reflection across the x - axis • (r_y): a reflection across the y - axis • (t_{-1,-7}): a translation so that ((x,y)\to(x - 1,y - 7)) which of these describes the sequence of transformations performed on △abc that results in △abc? a. (t_{-1,-7}) followed by (r_x) b. (t_{-1,-7}) followed by (r_y) c. (r_x) followed by (t_{-1,-7}) d. (r_y) followed by (t_{-1,-7})

Explanation:

Step1: Analyze reflection

First, observe that $\triangle ABC$ and $\triangle A'B'C'$ are symmetric about the y - axis. A reflection across the y - axis, $R_y$, changes the sign of the x - coordinate of each point, i.e., $(x,y)\to(-x,y)$.

Step2: Analyze translation

After reflection across the y - axis, we need to translate the triangle. The translation $T_{- 1,-7}$ moves each point 1 unit to the left and 7 units down, $(x,y)\to(x - 1,y - 7)$. If we first reflect across the y - axis and then apply the translation $T_{-1,-7}$, we get the correct transformation from $\triangle ABC$ to $\triangle A'B'C'$.

Answer:

D. $R_y$ followed by $T_{-1,-7}$