Question

fill in the blank 3 points
△xyz has vertices x(1,1), y(3,2), and z(-1,3). if △xyz is translated (x,y) -> (x - 2,y + 3), what are the vertices for the translated image?
x ( type your answer... , type your answer... )
y ( type your answer... , type your answer... )
z ( type your answer... , type your answer... )

Explanation:

Step1: Calculate \(X'\)

For point \(X(1,1)\), using the translation \((x,y)\to(x - 2,y+3)\).
\(x'=1-2=-1\), \(y'=1 + 3=4\). So \(X'(-1,4)\).

Step2: Calculate \(Y'\)

For point \(Y(3,2)\), \(x'=3-2 = 1\), \(y'=2+3=5\). So \(Y'(1,5)\).

Step3: Calculate \(Z'\)

For point \(Z(-1,3)\), \(x'=-1-2=-3\), \(y'=3 + 3=6\). So \(Z'(-3,6)\).

Answer:

\(X'(-1,4)\), \(Y'(1,5)\), \(Z'(-3,6)\)