Question

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

Explanation:

Step1: Determine the translation rule

By observing the graph, we can see that each point of \(\triangle ABC\) is translated \(3\) units to the right. The translation rule is \((x,y)\to(x + 3,y)\)

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

For point \(A(-2,3)\), using the rule \(x=-2+3 = 1\), \(y = 3\). So \(A'(1,3)\)

Step3: Apply the translation rule to point \(B\)

For point \(B(0,4)\), using the rule \(x=0 + 3=3\), \(y = 4\). So \(B'(3,4)\)

Step4: Apply the translation rule to point \(C\)

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

Answer:

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