Alg6.4

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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\,

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