Homework Help is Here – Start Your Trial Now!
Math
Geometry
2. Triangle ABC is graphed on a plane. The coordinates are A(-2,5), B(-8,5), and C(-2,-1). If A ABC is reflected over the line y = x, what are the coordinates of the vertices of A A'B'C'? B B. C A' = (2.5) (4,5) B' = C' =

2. Triangle ABC is graphed on a plane. The coordinates are A(-2,5), B(-8,5), and C(-2,-1). If A ABC is reflected over the line y = x, what are the coordinates of the vertices of A A'B'C'? B B. C A' = (2.5) (4,5) B' = C' =

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
Did I do it correctly?
**Triangle Reflection Exercise** In this exercise, you will explore the transformation of a triangle reflected over a given line in a coordinate plane. **Problem Statement:** Triangle \( \triangle ABC \) is graphed on a coordinate plane. The coordinates are as follows: - \( A(-2, 5) \) - \( B(-8, 5) \) - \( C(-2, -1) \) Task: Reflect \( \triangle ABC \) over the line \( y = x \). **Objectives:** Determine the coordinates of the vertices of the reflected triangle \( \triangle A'B'C' \). **Graphical Explanation:** The provided graph displays triangle \( \triangle ABC \) with the points labeled \( A \), \( B \), and \( C \). The triangle is oriented such that \( A \) and \( B \) are on the positive side of the y-axis, while \( C \) crosses the negative side. The line \( y = x \) serves as the axis of reflection. **reflection outcome:** After calculating the reflection of each point over the line \( y = x \): - \( A' = (5, -2) \) - \( B' = (5, -8) \) - \( C' = (-1, -2) \) These coordinates are derived through the process of swapping the x and y values of the original points, as reflecting over the line \( y = x \) involves this transformation. By understanding reflections and coordinate transformations, you gain fundamental skills in geometric analysis and spatial reasoning.
Transcribed Image Text:**Triangle Reflection Exercise** In this exercise, you will explore the transformation of a triangle reflected over a given line in a coordinate plane. **Problem Statement:** Triangle \( \triangle ABC \) is graphed on a coordinate plane. The coordinates are as follows: - \( A(-2, 5) \) - \( B(-8, 5) \) - \( C(-2, -1) \) Task: Reflect \( \triangle ABC \) over the line \( y = x \). **Objectives:** Determine the coordinates of the vertices of the reflected triangle \( \triangle A'B'C' \). **Graphical Explanation:** The provided graph displays triangle \( \triangle ABC \) with the points labeled \( A \), \( B \), and \( C \). The triangle is oriented such that \( A \) and \( B \) are on the positive side of the y-axis, while \( C \) crosses the negative side. The line \( y = x \) serves as the axis of reflection. **reflection outcome:** After calculating the reflection of each point over the line \( y = x \): - \( A' = (5, -2) \) - \( B' = (5, -8) \) - \( C' = (-1, -2) \) These coordinates are derived through the process of swapping the x and y values of the original points, as reflecting over the line \( y = x \) involves this transformation. By understanding reflections and coordinate transformations, you gain fundamental skills in geometric analysis and spatial reasoning.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 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