Question

congruence
which best explains whether or not triangles rst and acb are congruent?
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 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 does not correspond with point a.

Explanation:

• Reflection over the \(y\)-axis: Reflecting \(\triangle RST\) over the \(y\)-axis changes the \(x\)-coordinates of its vertices. For example, if a point \((x,y)\) in \(\triangle RST\) is reflected over the \(y\)-axis, it becomes \((-x,y)\).
• Translation 2 units down: After reflection, translating the reflected triangle 2 units down changes the \(y\)-coordinates of its vertices. If a point \((x,y)\) is translated 2 units down, it becomes \((x,y - 2)\).
• Congruence transformation: A reflection and a translation are rigid transformations. Rigid transformations preserve the shape and size of a figure. So, if \(\triangle RST\) can be mapped to \(\triangle ACB\) using a reflection over the \(y\)-axis and a translation 2 units down, then the two triangles are congruent.

Answer:

The figures are congruent. \(\triangle RST\) can be mapped to \(\triangle ACB\) by a reflection over the \(y\)-axis and a translation 2 units down.