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High School Math Geometry Geometry, Student Edition

The equation of the translated line.

The equation of the translated line.

Geometry, Student Edition

Geometry, Student Edition

1st Edition

ISBN: 9780078884849

Author: McGraw-Hill, McGraw Hill

Publisher: Glencoe/McGraw-Hill School Pub Co

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Question

Chapter 9.2, Problem 31HP

To determine

To find: The equation of the translated line.

Expert Solution & Answer

Answer to Problem 31HP

The equation of the translated line is $y=mx−am+2b$ .

Explanation of Solution

Given information:

The given information is a line $y=mx+b$ is translated using the vector $(a,b)$ .

Calculation:

We are given the line:

$y=mx+b$

The translation moves each point $(x,y)$ of the line in the point $(x+a,y+b)$ :

$y=00=mx+bx=−bm$

$x=0y=m×0+by=bx=−bm$

$A(0,b)B(−bm,0)$

We determine the x and y intercepts of the original line:

$A(0,b)→A'(0+a,b+b)=(a,2b)B(−bm,0)→B'(−bm+a,0+b)=(a−bm,b)$

We use the points $A$ , and $B'$ to determine the equation of the line's translation:

$m'=2b−ba−(a−bm)=bbm=m$

$y−yA'=m'(x−xA')y−2b=(x−a)y=mx−am+2b$

The $x$ and $y$ intercepts of the line’s translation are:

$x=0y=m×0−am+2b=2b−am$

$y=00=m×x−am+2bx=a−2bm$

Therefore, the equation of the translated line is $y=mx−am+2b$ .

Chapter 9.2, Problem 30HP

Chapter 9.2, Problem 32HP

Chapter 9 Solutions

Geometry, Student Edition

Ch. 9.1 - Prob. 1ACYP Ch. 9.1 - Prob. 1BCYP Ch. 9.1 - Prob. 1CCYP Ch. 9.1 - Prob. 2CYP Ch. 9.1 - Prob. 3ACYP Ch. 9.1 - Prob. 3BCYP Ch. 9.1 - Prob. 4ACYP Ch. 9.1 - Prob. 4BCYP Ch. 9.1 - Prob. 5CYP Ch. 9.1 - Prob. 1CYU

Ch. 9.1 - Prob. 2CYU Ch. 9.1 - Prob. 3CYU Ch. 9.1 - Prob. 4CYU Ch. 9.1 - Prob. 5CYU Ch. 9.1 - Prob. 6CYU Ch. 9.1 - Prob. 7CYU Ch. 9.1 - Prob. 8CYU Ch. 9.1 - Prob. 9CYU Ch. 9.1 - Prob. 10PPS Ch. 9.1 - Prob. 11PPS Ch. 9.1 - Prob. 12PPS Ch. 9.1 - Prob. 13PPS Ch. 9.1 - Prob. 14PPS Ch. 9.1 - Prob. 15PPS Ch. 9.1 - Prob. 16PPS Ch. 9.1 - Prob. 17PPS Ch. 9.1 - Prob. 18PPS Ch. 9.1 - Prob. 19PPS Ch. 9.1 - Prob. 20PPS Ch. 9.1 - Prob. 21PPS Ch. 9.1 - Prob. 22PPS Ch. 9.1 - Prob. 23PPS Ch. 9.1 - Prob. 24PPS Ch. 9.1 - Prob. 25PPS Ch. 9.1 - Prob. 26PPS Ch. 9.1 - Prob. 27PPS Ch. 9.1 - Prob. 28PPS Ch. 9.1 - Prob. 29PPS Ch. 9.1 - Prob. 30PPS Ch. 9.1 - Prob. 31PPS Ch. 9.1 - Prob. 32PPS Ch. 9.1 - Prob. 33PPS Ch. 9.1 - Prob. 34PPS Ch. 9.1 - Prob. 35PPS Ch. 9.1 - Prob. 36PPS Ch. 9.1 - Prob. 37PPS Ch. 9.1 - Prob. 38PPS Ch. 9.1 - Prob. 39PPS Ch. 9.1 - Prob. 40PPS Ch. 9.1 - Prob. 41PPS Ch. 9.1 - Prob. 42PPS Ch. 9.1 - Prob. 43PPS Ch. 9.1 - Prob. 44PPS Ch. 9.1 - Prob. 45HP Ch. 9.1 - Prob. 46HP Ch. 9.1 - Prob. 47HP Ch. 9.1 - 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Prob. 55SR Ch. 9 - Prob. 1GRFC Ch. 9 - Prob. 2GRFC Ch. 9 - Prob. 3GRFC Ch. 9 - Prob. 4GRFC Ch. 9 - Prob. 5GRFC Ch. 9 - Prob. 6GRFC Ch. 9 - Prob. 7GRFC Ch. 9 - Prob. 8GRFC Ch. 9 - Prob. 1MCQ Ch. 9 - Prob. 2MCQ Ch. 9 - Prob. 3MCQ Ch. 9 - Prob. 4MCQ Ch. 9 - Prob. 5MCQ Ch. 9 - Prob. 6MCQ Ch. 9 - Prob. 7MCQ Ch. 9 - Prob. 8MCQ Ch. 9 - Prob. 9MCQ Ch. 9 - Prob. 10MCQ Ch. 9 - Prob. 11MCQ Ch. 9 - Prob. 12MCQ Ch. 9 - Prob. 13MCQ Ch. 9 - Prob. 14MCQ Ch. 9 - Prob. 15MCQ Ch. 9 - Prob. 1SGR Ch. 9 - Prob. 2SGR Ch. 9 - Prob. 3SGR Ch. 9 - Prob. 4SGR Ch. 9 - Prob. 5SGR Ch. 9 - Prob. 6SGR Ch. 9 - Prob. 7SGR Ch. 9 - Prob. 8SGR Ch. 9 - Prob. 9SGR Ch. 9 - Prob. 10SGR Ch. 9 - Prob. 11SGR Ch. 9 - Prob. 12SGR Ch. 9 - Prob. 13SGR Ch. 9 - Prob. 14SGR Ch. 9 - Prob. 15SGR Ch. 9 - Prob. 16SGR Ch. 9 - Prob. 17SGR Ch. 9 - Prob. 18SGR Ch. 9 - Prob. 19SGR Ch. 9 - Prob. 20SGR Ch. 9 - Prob. 21SGR Ch. 9 - Prob. 22SGR Ch. 9 - Prob. 23SGR Ch. 9 - Prob. 24SGR Ch. 9 - Prob. 25SGR Ch. 9 - Prob. 26SGR Ch. 9 - Prob. 27SGR Ch. 9 - 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