Homework Help is Here – Start Your Trial Now!
Math
Geometry
Given points J(1, 4), A(3, 5), and G(2, 1), what are the coordinates of AJ'A'G' when reflected over the line y=2?

Given points J(1, 4), A(3, 5), and G(2, 1), what are the coordinates of AJ'A'G' when reflected over the line y=2?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
See similar textbooks
icon
Related questions
Question

i need J' A' G'

**Reflection of Triangle Over a Line** **Problem Statement:** Given points \( J(1, 4) \), \( A(3, 5) \), and \( G(2, 1) \), what are the coordinates of \( \triangle J'A'G' \) when reflected over the line \( y = 2 \)? **Explanation:** To find the coordinates of the reflected points, use the reflection formula across the line \( y = k \). The formula for reflecting a point \( (x, y) \) over the line \( y = k \) is \( (x, 2k - y) \). **Reflection Steps:** 1. **Reflect Point \( J(1, 4) \):** - Original y-coordinate: 4 - Line of reflection y-coordinate: 2 - Reflected y-coordinate: \( 2 \times 2 - 4 = 0 \) - Reflected point \( J'(1, 0) \) 2. **Reflect Point \( A(3, 5) \):** - Original y-coordinate: 5 - Line of reflection y-coordinate: 2 - Reflected y-coordinate: \( 2 \times 2 - 5 = -1 \) - Reflected point \( A'(3, -1) \) 3. **Reflect Point \( G(2, 1) \):** - Original y-coordinate: 1 - Line of reflection y-coordinate: 2 - Reflected y-coordinate: \( 2 \times 2 - 1 = 3 \) - Reflected point \( G'(2, 3) \) The reflected coordinates of \( \triangle J'A'G' \) are: - \( J'(1, 0) \) - \( A'(3, -1) \) - \( G'(2, 3) \)
Transcribed Image Text:**Reflection of Triangle Over a Line** **Problem Statement:** Given points \( J(1, 4) \), \( A(3, 5) \), and \( G(2, 1) \), what are the coordinates of \( \triangle J'A'G' \) when reflected over the line \( y = 2 \)? **Explanation:** To find the coordinates of the reflected points, use the reflection formula across the line \( y = k \). The formula for reflecting a point \( (x, y) \) over the line \( y = k \) is \( (x, 2k - y) \). **Reflection Steps:** 1. **Reflect Point \( J(1, 4) \):** - Original y-coordinate: 4 - Line of reflection y-coordinate: 2 - Reflected y-coordinate: \( 2 \times 2 - 4 = 0 \) - Reflected point \( J'(1, 0) \) 2. **Reflect Point \( A(3, 5) \):** - Original y-coordinate: 5 - Line of reflection y-coordinate: 2 - Reflected y-coordinate: \( 2 \times 2 - 5 = -1 \) - Reflected point \( A'(3, -1) \) 3. **Reflect Point \( G(2, 1) \):** - Original y-coordinate: 1 - Line of reflection y-coordinate: 2 - Reflected y-coordinate: \( 2 \times 2 - 1 = 3 \) - Reflected point \( G'(2, 3) \) The reflected coordinates of \( \triangle J'A'G' \) are: - \( J'(1, 0) \) - \( A'(3, -1) \) - \( G'(2, 3) \)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS