Given (-5, 15) and (-5, 9), find the midpoint, distance, slope, and equation of the line.

(Last Updated On: December 13, 2017)

Problem: Given these pairs of points, (-5, 15) and (-5, 9), find the midpoint, distance, slope, and equation of the line.

(-5,15),(-5,9),

Solutions:

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

left(frac{-5-5}{2},frac{15+9}{2}right) = left(-5,frac{15+9}{2}right) = left(-5,frac{15+9}{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{(-5+5)^2+(15-9)^2} = sqrt{0^2+6^2} = sqrt{6^2} = 6,

  • To find the slope, use the formula

 m = frac{y_2-y_1}{x_2-x_1},

m = frac{9-15}{-5-(-5)} = undefined, (which means it is a vertical line, which has infinite slope)
  • Since the line is vertical, there is only one x value that will give all y values. The equation for the line is

x = -5,

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    credit: Todd©2013 www.FroydWess.com
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