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 point \( Q' \), we apply the translation given by the transformation \( (x,y) \to (x+7, y-5) \) to the coordinates of the point \( Q(0,6) \).

Starting with the coordinates of point \( Q \):
- \( x = 0 \)
- \( y = 6 \)

Applying the translation:
1. For the \( x \)-coordinate, we calculate:
\[
x' = x + 7 = 0 + 7 = 7
\]

2. For the \( y \)-coordinate, we calculate:
\[
y' = y - 5 = 6 - 5 = 1
\]

Thus, the coordinates of point \( Q' \) after the translation are:
\[
Q' = (7, 1)
\]

Therefore, the coordinates of \( Q' \) are \( \boxed{(7, 1)} \).