Question

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

Explanation:

Step1: Find the translation rule

To find the translation rule, compare the coordinates of \(A(-2,3)\) and \(A'(1,3)\).
The \(y -\)coordinate remains the same (\(y = 3\)), and for the \(x -\)coordinate: \(x\) changes from \(-2\) to \(1\). The rule for the \(x -\)translation is \(x'=x + 3\) (since \(1-(-2)=3\)).

Step2: Apply the translation rule to \(B(0,4)\)

For point \(B\), using the rule \(x'=x + 3\) and \(y'=y\) (because the \(y -\)coordinate of \(A\) and \(A'\) is the same).
If \(x = 0\) and \(y = 4\), then \(x'=0 + 3=3\) and \(y'=4\). So \(B'\) has coordinates \((3,4)\).

Step3: Apply the translation rule to \(C(1,1)\)

For point \(C\), using the rule \(x'=x + 3\) and \(y'=y\).
If \(x = 1\) and \(y = 1\), then \(x'=1+ 3=4\) and \(y'=1\). So \(C'\) has coordinates \((4,1)\).

Answer:

\(\triangle ABC\)	\(\triangle A'B'C'\)
\(B(0,4)\)	\(B'(3,4)\)
\(C(1,1)\)	\(C'(4,1)\)