Question

the vertices of $\triangle abc$ are $a(-1, 1)$, $b(4, 2)$, and $c(1, 5)$. the vertices of $\triangle def$ are $d(-1, -1)$, $e(4, -2)$ and $f(1, -5)$ such that $\triangle abc \cong \triangle def$. identify the congruence transformation.
reflection in the
select choice

Explanation:

Step1: Analyze Coordinate Changes

Compare coordinates of \( \triangle ABC \) (A(-1,1), B(4,2), C(1,5)) and \( \triangle DEF \) (D(-1,-1), E(4,-2), F(1,-5)). Notice that for each point \((x,y)\) in \( \triangle ABC \), the corresponding point in \( \triangle DEF \) is \((x, -y)\).

Step2: Identify Transformation

The transformation \((x,y) \to (x, -y)\) is a reflection over the x - axis. This is because reflecting a point \((x,y)\) over the x - axis changes the sign of the y - coordinate while keeping the x - coordinate the same.

Answer:

Reflection in the x - axis