Question
y 7- 6- 5 4- 3 2- 1 COURSE TOOLS axis of reflection - 7-6-5-4-3-2-10 -1+ -2 -0+ Item 2 1 2 3 4 5 LESSON FEEDBACK 6 7 X (1,-1) Z (6,0) < -3- -4- < x page 18 of 18 > Item 3 Item 4 Item 5 COURSE OUTLINE Y (4,3) y=1What are the coordinates of Y' after a reflection across y = 1? (1 point) ΟΥ' (-2,-1) ΟΥ' (4,-1) Y'(-2,3) ΟΥ' (4,5)
Answers
GPT-4o mini
To find the coordinates of point Y (4, 3) after reflecting across the line y = 1, we need to determine how far Y is from y = 1, and then find the corresponding point on the opposite side of the line.
1. **Determine the distance from Y to the line y = 1:**
- The y-coordinate of Y is 3.
- The distance from Y(4, 3) to the line y = 1 is calculated as:
\[
3 - 1 = 2
\]
2. **Reflect Y across y = 1:**
- Since Y is 2 units above the line y = 1, the reflected point Y' will be 2 units below y = 1.
- The y-coordinate of Y' will be:
\[
1 - 2 = -1
\]
- The x-coordinate remains the same: 4.
So, the coordinates of Y' after reflection across the line y = 1 are **Y' (4, -1)**.
Among the choices you provided, the correct answer is **Y' (4, -1)**.
1. **Determine the distance from Y to the line y = 1:**
- The y-coordinate of Y is 3.
- The distance from Y(4, 3) to the line y = 1 is calculated as:
\[
3 - 1 = 2
\]
2. **Reflect Y across y = 1:**
- Since Y is 2 units above the line y = 1, the reflected point Y' will be 2 units below y = 1.
- The y-coordinate of Y' will be:
\[
1 - 2 = -1
\]
- The x-coordinate remains the same: 4.
So, the coordinates of Y' after reflection across the line y = 1 are **Y' (4, -1)**.
Among the choices you provided, the correct answer is **Y' (4, -1)**.