Question

Point
\[Q'\] is the image of
\[Q(0,6)\] under the translation
\[(x,y)\to(x+7,y-5)\].

What are the coordinates of
\[Q'\]?

Answer 1

To find the coordinates of the image point $Q'$, we can apply the translation rule $(x,y)\to(x+7,y-5)$ to the coordinates of $Q(0,6)$. Substituting these values into the rule, we get \begin{align*}
x+7&=0, \\
y-5&=6.
\end{align*}Solving the first equation for $x$, we have $x=-7$. Solving the second equation for $y$, we find $y=11$. Thus, $Q' = \boxed{(-7,11)}$.