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 \( H^{\prime} \) ? \( (7,-8) \) \( (-7,6) \) \( (3,-12) \) \( (2,1) \)
Ask by Parry Lewis. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The coordinates of \( H' \) are \((-7, 6)\).
Solution
To find the coordinates of \( H' \) after the translation \( T_{-5,9}(x, y) \), follow these steps:
1. **Understand the Translation Rule:**
The translation rule \( T_{-5,9}(x, y) \) means that every point \((x, y)\) is moved by \(-5\) units in the \(x\)-direction and \(+9\) units in the \(y\)-direction.
2. **Apply the Translation to Point \( H \):**
The pre-image of point \( H \) is \((-2, -3)\). Applying the translation:
\[
H' = (x - 5, y + 9) \\
H' = (-2 - 5, -3 + 9) \\
H' = (-7, 6)
\]
**Answer:**
\((-7,\ 6)\)
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Simplify this solution Mind Expander
To find the coordinates of point \( H' \) after the translation \( T_{-5,9}(x, y) \), we apply the translation rule to the coordinates of point \( H \) which are \( (-2, -3) \). The translation rule works as follows: - \( x' = x + (-5) \) - \( y' = y + 9 \) Applying this to point \( H \): 1. For the x-coordinate: \[ x' = -2 - 5 = -7 \] 2. For the y-coordinate: \[ y' = -3 + 9 = 6 \] Thus, the coordinates of \( H' \) are \( (-7, 6) \). So the correct answer is: \( (-7,6) \)
