BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 10.5, Problem 7E

To determine

To find: The distance from the given point A to the given line.

Expert Solution & Answer

Answer to Problem 7E

The distance from the given point A to the given line is 1010 units .

Explanation of Solution

Given information:

The given point A is A(−1,4) , the slope of the line is −3 and passes through (2,−4) .

The y -intercept of the line is obtained as,

y=mx+c−4=(−3)(2)+cc=2

The equation of the line will be,

y=mx+cy=(−3)x+2y=−3x+2

The slope of the perpendicular line on the given line will be 13 .

The y -intercept of the perpendicular equation on the given line from point A is obtain as,

y=mx+c4=(13)(−1)+cc=133

The equation of the perpendicular line will be,

y=mx+cy=(13)x+1333y=x+13

The intersection point of the lines is at (−710,4110) .

Calculate the distance from the given point A to the given line that is point (−710,4110) ,

d=(x2−x1)2+(y2−y1)2=(−710−(−1))2+(4110−4)2=1010 units

Thus, the distance from the given point A to the given line is 1010 units .

Chapter 10.5, Problem 6E

Chapter 10.5, Problem 8E

Chapter 10 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

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