Question

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

Explanation:

Step1: Determine the transformation rule

From \(A(-2,3)\) to \(A'(1,3)\), the \(x\) - coordinate changes from \(-2\) to \(1\) (\(-2 + 3=1\)), and the \(y\) - coordinate remains the same (\(y = 3\)). So the transformation is a translation of \(3\) units to the right (since \(x\) - value increases by \(3\) and \(y\) - value is unchanged). The rule is \((x,y)\to(x + 3,y)\)

Step2: Apply the transformation rule to point \(B\)

For point \(B(0,4)\), using the rule \((x,y)\to(x + 3,y)\). Substitute \(x = 0\) and \(y = 4\) into the rule: \(x+3=0 + 3=3\), \(y = 4\). So \(B'\) has coordinates \((3,4)\)

Step3: Apply the transformation 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: \(x + 3=1+3 = 4\), \(y = 1\). So \(C'\) has coordinates \((4,1)\)

Answer:

\(B'(3,4)\), \(C'(4,1)\)