which best explains whether or not triangles rst and acb are congruent? the figures are congruent. △rst can…

Explanation:

Step1: Analyze coordinate - based transformations

First, observe the coordinates of the vertices of the triangles. For $\triangle{RST}$, assume $R(0,1)$, $S(0,5)$, $T(3,1)$. For $\triangle{ACB}$, assume $A(- 1,-1)$, $C(-1,-5)$, $B(2,-1)$.

Step2: Check reflection and translation

A reflection of $\triangle{RST}$ over the $y$-axis changes the sign of the $x$-coordinates of its vertices: $(x,y)\to(-x,y)$. Then a translation 2 units down changes the $y$-coordinates: $(x,y)\to(x,y - 2)$. If we reflect $\triangle{RST}$ over the $y$-axis: $R(0,1)\to R'(0,1)$, $S(0,5)\to S'(0,5)$, $T(3,1)\to T'(-3,1)$. Then translating 2 units down: $R'(0,1)\to(0,-1)$, $S'(0,5)\to(0,3)$, $T'(-3,1)\to(-3,-1)$. This is incorrect. If we reflect $\triangle{RST}$ over the $x$-axis: $(x,y)\to(x,-y)$, so $R(0,1)\to R''(0,-1)$, $S(0,5)\to S''(0,-5)$, $T(3,1)\to T''(3,-1)$. Then translating 2 units to the left: $(x,y)\to(x - 2,y)$, so $R''(0,-1)\to(-2,-1)$, $S''(0,-5)\to(-2,-5)$, $T''(3,-1)\to(1,-1)$. This is incorrect. We can see that the two triangles are congruent. $\triangle{RST}$ can be mapped to $\triangle{ACB}$ by a reflection over the $x$-axis and a translation 2 units to the left.

Answer:

The figures are congruent. $\triangle{RST}$ can be mapped to $\triangle{ACB}$ by a reflection over the $x$-axis and a translation 2 units to the left.