Question
\( D \) and \( R \) are points on a polygon. \( D^{\prime} \) and \( R^{\prime} \) are the points under a translation. Find \( R^{\prime} \) \( D(6,-10) \) \( D^{\prime}(15,-9) \) \( R(12,-1) \)
Ask by Robbins Wagner. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( R^{\prime} = (21,\ 0) \)
Solution
To find the coordinates of \( R' \) under the same translation that maps \( D \) to \( D' \), follow these steps:
1. **Determine the Translation Vector:**
The translation moves point \( D(6, -10) \) to \( D'(15, -9) \). The translation vector \((a, b)\) can be found by subtracting the coordinates of \( D \) from \( D' \):
\[
a = 15 - 6 = 9
\]
\[
b = -9 - (-10) = 1
\]
So, the translation vector is \((9, 1)\).
2. **Apply the Translation to Point \( R \):**
To find \( R' \), add the translation vector to the coordinates of \( R(12, -1) \):
\[
R'_x = 12 + 9 = 21
\]
\[
R'_y = -1 + 1 = 0
\]
Therefore, \( R' \) is at \((21, 0)\).
**Answer:** \( R^{\prime} = (21,\ 0) \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find \( R^{\prime} \), we need to determine the translation applied to point \( D \) to get to point \( D^{\prime} \). 1. First, identify the translation vector: \[ \text{Translation} = D^{\prime} - D = (15 - 6, -9 - (-10)) = (9, 1) \] 2. Now, apply the same translation vector to point \( R \): \[ R^{\prime} = R + \text{Translation} = (12, -1) + (9, 1) = (12 + 9, -1 + 1) = (21, 0) \] Thus, the coordinates of \( R^{\prime} \) are \( (21, 0) \).
