Alg6.4

For these pairs of points, find the midpoint, distance, slope, and equation of the line.

$(-5,15),(-5,9)\,$

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

$x = -5\,$