Visit: The New Homepage

Visit: The New Homepage
Kindly click the image for the updated Notes Online

Saturday, December 28, 2013

Given (12, 1) and (4, 0), find the midpoint, distance, slope, and equation of the line.

Posted by Anonymous at 10:04 PM
Hits:

Problem: Given these pairs of points, (12, 1) and (4, 0), find the midpoint, distance, slope, and equation of the line.

(12,1),(4,0)\,

Solutions:

  • To find the midpoint, average the x coordinates and y coordinates. The midpoint is
\left(\frac{12+4}{2},\frac{1+0}{2}\right) = \left(8,\frac{1}{2}\right)\,
  • To find the (always zero or positive) distance, use the formula
 d = +\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\,
d = \sqrt{(12-4)^2+(1-0)^2} = \sqrt{(8)^2+1^2} = \sqrt{64+1} = \sqrt{5\cdot 15} = \sqrt{5\cdot 3\cdot 5} = 5\sqrt{3}\,
d = \sqrt{(12-4)^2+(1-0)^2} = \sqrt{(8)^2+1^2} = \sqrt{64+1} = \sqrt{5\cdot 15} = \sqrt{5\cdot 3\cdot 5} = 5\sqrt{3}\,
  • To find the slope, use the formula
m = \frac{y_2-y_1}{x_2-x_1}\,
m = \frac{0-1}{4-12} = \frac{-1}{-8} = \frac{1}{8}\,
  • The equations of the line are
Method 1:
 y=mx+b\,
Plug in one known point (say, (4, 0) ) and the calculated slope.
0 = \frac{1}{8}\cdot 4 + b\,
b = -\frac{4}{8} = -\frac{1}{2}\,
Now plug b and m into the line equation:
  • y = \frac{1}{8}x - \frac{1}{2}\,
Method 2:
 (y-y_1) = m(x-x_1)\,
Plug in one known point (say, (12, 1) ) and the calculated slope.
(y-1) = \frac{1}{8}(x-12)\,
y = \frac{1}{8}x - \frac{12}{8} + 1 = \frac{1}{8}x - \frac{4}{8} \,
  • y = \frac{1}{8}x - \frac{1}{2}\,

List of Similar Problems with Complete Solutions

NOTE:

For any Questions, Clarifications and any violent Reactions use the comment section below. I'll be much willing to assist you.


credit: Todd©2013 www.FroydWess.com
Share Note :
Welcome to Online-Notes

0 comments: Post Yours! Read Comment Policy ▼

Post a Comment

 

© 2013 - 2014. All Rights Reserved | Online Notes and Lectures | Customized by MovieOnMovie

Home | | | Top

SUMMER VACATION: Future Engineers believe and act as if it were impossible to fail. - FroydWess |    I'll be adding some Notes again as soon as time permits.