Given (4, 13) and (0, 9), find the midpoint, distance, slope, and equation of the line.

(Last Updated On: December 13, 2017)

Problem: Given these pairs of points, (4, 13) and (0, 9), find the midpoint, distance, slope, and equation of the line.

(4,13),(09,0),

Solutions:

  • To find the midpoint, average the x coordinates and y coordinates. The midpoint is

left(frac{4+0}{2},frac{13+9}{2}right) = (2,11),

  • 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{(4-0)^2+(13-9)^2} = sqrt{(4)^2+4^2} = sqrt{16+16} = sqrt{16*2} = sqrt{4*4*2} = 4sqrt{2},
d = sqrt{(4-0)^2+(13-9)^2} = sqrt{(4)^2+4^2} = sqrt{16+16} = sqrt{16*2} = sqrt{4*4*2} = 4sqrt{2},

  • To find the slope, use the formula

 m = frac{y_2-y_1}{x_2-x_1},
m = frac{9-13}{0-4} = frac{-4}{-4} = 1,

  • The equations of the line are

Method 1:
 y=mx+b,
Plug in one known point (say, (0, 9)) and the calculated slope.
9 = 0 + b,
b = 9,
Now plug b and m into the line equation:

  • y = x + 9,

Method 2:
 (y-y_1) = m(x-x_1),

Plug in one known point (say, (4, 13)) and the calculated slope.

(y-13) = (x-4),
y = x + 9,

  • y = x + 9,

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
Given (4, 13) and (0, 9), find the midpoint, distance, slope, and equation of the line.
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