Question

Suppose triangle XYZ has vertices X¢(-1, -7), Y¢(-2,0), and Z¢(-3,4) after being translated 2 units down and 5 units left. What were the original coordinates of triangle XYZ?

Answer 1

$\begin{gathered} \text{translation means in this case that} \\ (x,y)\Rightarrow(x-5,y-2) \\ In\text{ order to return to the original position, we must invert the translation:} \\ (x^{\prime},y^{\prime})\Rightarrow(x^{\prime}+5,y^{\prime}+2) \end{gathered}$$\begin{gathered} \text{Therefore,} \\ \text{(-1,-7)}\Rightarrow(-1+5,-7+2)\Rightarrow(4,-5) \\ \text{(-2,0)}\Rightarrow(-2+5,0+2)\Rightarrow(3,2) \\ \text{(-3,4)}\Rightarrow(-3+5,4+2)\Rightarrow(2,6) \end{gathered}$$\begin{gathered} originalcoordinatesoftriangleXYZ\text{ are} \\ X=(4,-5) \\ Y=(3,2) \\ Z=(2,6) \end{gathered}$