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

Saturday, December 28, 2013

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

Posted by Unknown at 10:55 PM

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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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Tags: distance, equation of line, Geometry Problems, midpoint, slope

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Saturday, December 28, 2013