Question
Rectangle EFGH is translated according to the rule T–5, 9(x, y). If the coordinates of the pre-image of point H are (–2, –3), what are the coordinates of H'?
(7, –8)
(–7, 6)
(3, –12)
(2, 1)
(7, –8)
(–7, 6)
(3, –12)
(2, 1)
Answers
GPT-4o mini
To translate rectangle EFGH according to the rule \( T_{-5, 9}(x, y) \), we can apply the translation to the coordinates of point H.
The translation rule \( T_{-5, 9} \) means that you subtract 5 from the x-coordinate and add 9 to the y-coordinate of the point.
The coordinates of the pre-image of point H are \((-2, -3)\).
Now let's apply the translation:
1. For the x-coordinate:
\[
x' = -2 - 5 = -7
\]
2. For the y-coordinate:
\[
y' = -3 + 9 = 6
\]
Thus, the coordinates of H' after the translation are \((-7, 6)\).
So the answer is:
\[
\boxed{(-7, 6)}
\]
The translation rule \( T_{-5, 9} \) means that you subtract 5 from the x-coordinate and add 9 to the y-coordinate of the point.
The coordinates of the pre-image of point H are \((-2, -3)\).
Now let's apply the translation:
1. For the x-coordinate:
\[
x' = -2 - 5 = -7
\]
2. For the y-coordinate:
\[
y' = -3 + 9 = 6
\]
Thus, the coordinates of H' after the translation are \((-7, 6)\).
So the answer is:
\[
\boxed{(-7, 6)}
\]