Question

a sequence of transformations is performed on △abc, resulting in △abc. both triangles are shown in the coordinate plane below. some transformations are listed below. • rx: a reflection across the x - axis • ry: a reflection across the y - axis • t - 1, - 2: a translation so that (x, y)→(x - 1,y - 2) which of these describes the sequence of transformations performed on △abc that results in △abc? a. t - 1, - 2 followed by rx b. t - 1, - 2 followed by ry c. rx followed by t - 1, - 2 d. ry followed by t - 1, - 2

Explanation:

Step1: Analyze reflection across x - axis

A reflection across the x - axis changes the sign of the y - coordinate of each point. If we first reflect $\triangle ABC$ across the x - axis, the points will be in a position where they are upside - down relative to the original triangle.

Step2: Analyze translation

The translation $T_{-1,-2}$ moves each point $(x,y)$ to $(x - 1,y - 2)$. If we apply this translation after the reflection across the x - axis, we can match the position of $\triangle A'B'C'$.

Step3: Check option C

Option C says $R_x$ followed by $T_{-1,-2}$. First, reflecting across the x - axis flips the triangle over the x - axis. Then, translating 1 unit to the left and 2 units down will result in the position of $\triangle A'B'C'$.

Answer:

C. $R_x$ followed by $T_{-1,-2}$