Question

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complete the table to show the coordinates of the vertices of \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\).

Explanation:

Step1: Determine 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: \(x\) value of \(A'\) is \(x\) value of \(A\) plus \(3\) (\(1-(-2)=3\)). So the translation rule is \((x,y)\to(x + 3,y)\).

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

Using the rule \((x,y)\to(x + 3,y)\), for \(B(0,4)\):
\(x=0+3 = 3\), \(y = 4\). So \(B'\) has coordinates \((3,4)\).

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

Using the rule \((x,y)\to(x + 3,y)\), for \(C(1,1)\):
\(x=1 + 3=4\), \(y = 1\). So \(C'\) has coordinates \((4,1)\).

Answer:

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