Question

which best explains whether or not triangles rst and acb are congruent? the figures are congruent. △rst can be mapped to △acb by a reflection over the x - axis and a translation 2 units to the left. the figures are not congruent. point r corresponds to point a, but s corresponds to b and t corresponds to c. the figures are congruent. △rst can be mapped to △acb by a reflection over the y - axis and a translation 2 units down. the figures are not congruent. point r does not correspond with point a

Explanation:

Step1: Recall congruence criteria

Two triangles are congruent if they can be mapped onto each other through rigid - motions (reflections, translations, rotations).

Step2: Analyze the first option

For $\triangle RST$ to be mapped to $\triangle ACB$ by a reflection over the $x$ - axis, the $y$ - coordinates of the vertices of $\triangle RST$ will change their signs. Then a translation 2 units to the left will change the $x$ - coordinates.
Let the coordinates of $R=(1,1)$, $S=(1,5)$, $T=(4,1)$. After reflection over the $x$ - axis, the coordinates become $R'=(1, - 1)$, $S'=(1,-5)$, $T'=(4,-1)$. After translation 2 units to the left, the coordinates become $R''=(-1,-1)$, $S''=(-1,-5)$, $T''=(2,-1)$.
Let the coordinates of $A = (-1,-1)$, $B=(2,-1)$, $C=(-1,-5)$. We can see that $\triangle RST$ can be mapped to $\triangle ACB$ by a reflection over the $x$ - axis and a translation 2 units to the left.

Step3: Analyze other options

The second option is wrong because we can find a correct correspondence. The third option is wrong as a reflection over the $y$ - axis and translation 2 units down will not map $\triangle RST$ to $\triangle ACB$. The fourth option is wrong as point $R$ can correspond to point $A$ under the correct rigid - motion.

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.