Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 4, Problem 5E
To determine

To calculate: The x -coordinate of the point A if the image is rotated 90 degrees counterclockwise then reflected over the line y=x .

  Algebra 2, Chapter 4, Problem 5E , additional homework tip  1

Expert Solution & Answer
Check Mark

Answer to Problem 5E

The x -coordinate of the point Ais 2 .

Explanation of Solution

Given information:

The image is rotated 90 degrees counterclockwise then reflected over the line y=x .

  Algebra 2, Chapter 4, Problem 5E , additional homework tip  2

Calculation:

Consider the image is rotated 90 degrees counterclockwise then reflected over the line y=x .

  Algebra 2, Chapter 4, Problem 5E , additional homework tip  3

The coordinates of polygon DABC are A(2,2),B(2,2),C(3,1) and D(2,5) .

The vertex matrix form is provided below,

  [22322215]

According to the question the polygon is rotated 90 degrees counterclockwise about the origin.

For the new coordinates of the polygon the old vertex matrix must be multiplied with [0110]

Therefore,

  [0110][22322215]=[020+201052+02+03+02+0]=[22152232]

Now, the polygon is reflected over the line y=x so multiply the matrix by [0110] .

  [0110][22152232]=[0+20+203022+02+01+05+0]=[22322215]

Now, new coordinates are A(2,2),B(2,2),C(3,1) and D(2,5)

Thus, the x -coordinate of the point Ais 2 .

Chapter 4 Solutions

Algebra 2

Ch. 4.1 - Prob. 7CYUCh. 4.1 - Prob. 8CYUCh. 4.1 - Prob. 9PPSCh. 4.1 - Prob. 10PPSCh. 4.1 - Prob. 11PPSCh. 4.1 - Prob. 12PPSCh. 4.1 - Prob. 13PPSCh. 4.1 - Prob. 14PPSCh. 4.1 - Prob. 15PPSCh. 4.1 - Prob. 16PPSCh. 4.1 - Prob. 17PPSCh. 4.1 - Prob. 18PPSCh. 4.1 - Prob. 19PPSCh. 4.1 - Prob. 20PPSCh. 4.1 - Prob. 21PPSCh. 4.1 - Prob. 22PPSCh. 4.1 - Prob. 23PPSCh. 4.1 - Prob. 24PPSCh. 4.1 - Prob. 25PPSCh. 4.1 - Prob. 26PPSCh. 4.1 - Prob. 27PPSCh. 4.1 - Prob. 28PPSCh. 4.1 - Prob. 29PPSCh. 4.1 - Prob. 30PPSCh. 4.1 - Prob. 31PPSCh. 4.1 - Prob. 32PPSCh. 4.1 - Prob. 33PPSCh. 4.1 - Prob. 34PPSCh. 4.1 - Prob. 35HPCh. 4.1 - Prob. 36HPCh. 4.1 - Prob. 37HPCh. 4.1 - Prob. 38HPCh. 4.1 - Prob. 39HPCh. 4.1 - Prob. 40HPCh. 4.1 - Prob. 41HPCh. 4.1 - Prob. 42HPCh. 4.1 - Prob. 43HPCh. 4.1 - Prob. 44HPCh. 4.1 - Prob. 45STPCh. 4.1 - Prob. 46STPCh. 4.1 - Prob. 47STPCh. 4.1 - Prob. 48STPCh. 4.1 - Prob. 49STPCh. 4.1 - Prob. 50STPCh. 4.1 - Prob. 51STPCh. 4.1 - Prob. 52STPCh. 4.1 - Prob. 53SCh. 4.1 - Prob. 54SCh. 4.1 - 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