Question

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

Explanation:

Step1: Analyze coordinate - change pattern

For point \(A(-1,1)\) and \(D(-1, - 1)\), \(x\) - coordinate remains the same and \(y\) - coordinate changes sign. For \(B(4,2)\) and \(E(4,-2)\), \(x\) - coordinate is the same and \(y\) - coordinate changes sign. For \(C(1,5)\) and \(F(1,-5)\), \(x\) - coordinate is the same and \(y\) - coordinate changes sign.

Step2: Recall reflection rules

The rule for a reflection in the \(x\) - axis is \((x,y)\to(x, - y)\). Since the \(x\) - coordinates of the corresponding vertices of \(\triangle ABC\) and \(\triangle DEF\) are the same and the \(y\) - coordinates are opposite, the congruence transformation is a reflection in the \(x\) - axis.

Answer:

\(x\) - axis