Question
15. What is the image of the point \( A(-2,8) \) after a translation along vector \( (5,-10) \) \( (-7,-2) \) \( (3,18) \) \( (3,-2) \) \( (-12,18) \)
Ask by Henry Cross. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The image of point \( A(-2, 8) \) after translating by vector \( (5, -10) \) is \( (3, -2) \).
Solution
To find the image of the point \( A(-2, 8) \) after a translation along the vector \( (5, -10) \), you can use the following formula for translation:
\[
\text{New point} = (x + a, y + b)
\]
where \( (a, b) \) is the translation vector.
Given:
- Original point \( A(-2, 8) \)
- Translation vector \( (5, -10) \)
Applying the formula:
\[
x' = -2 + 5 = 3
\]
\[
y' = 8 + (-10) = -2
\]
So, the image of the point \( A \) after the translation is \( (3, -2) \).
**Answer:** \( \boxed{(3,\ -2)} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the image of the point \( A(-2,8) \) after a translation along the vector \( (5,-10) \), we add the components of the vector to the coordinates of the point. Starting with \( A(-2,8) \): - Add 5 to the x-coordinate: \(-2 + 5 = 3\) - Subtract 10 from the y-coordinate: \(8 - 10 = -2\) So, the image of point \( A \) after the translation is \( (3,-2) \). Therefore, the correct answer is \( (3,-2) \).
