Question

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

Explanation:

Step1: Check congruence by transformation

Congruent triangles can be mapped onto each other through rigid transformations (reflection, translation, rotation).

Step2: Analyze reflection and translation

• Reflect \(\triangle RST\) over the \(x -\)axis. The \(y -\)coordinates of its vertices change sign.
• Then translate 2 units to the left (subtract 2 from \(x -\)coordinates).
• After these transformations, \(\triangle RST\) maps to \(\triangle ACB\) as their side lengths and angles match (by counting grid units for side lengths in the coordinate - plane).

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.