Question

complete the table to show the coordinates of the vertices of △abc. △abc △abc a(-2,3) a(1,3) b(0,4) b(3,4) c(1,1) ? c(1,3) c(4,1) c(3,4)

Explanation:

Step1: Determine the translation rule

From \(A(-2,3)\) to \(A'(1,3)\), the \(x\) - coordinate changes: \(1-(-2)=3\), and the \(y\) - coordinate remains the same (\(3 - 3=0\)). The translation rule is \((x,y)\to(x + 3,y)\).

Step2: Apply the translation rule to point \(C\)

For point \(C(1,1)\), using the rule \((x,y)\to(x + 3,y)\).
Substitute \(x = 1\) and \(y = 1\) into the rule:
The \(x\) - coordinate of \(C'\) is \(1+3=4\), and the \(y\) - coordinate of \(C'\) is \(1\).

Answer:

\(C'(4,1)\)