# Distance and Midpoint Formulas for Points on the Coordinate Plane

The distance between two points is the same as the length of the hypotenuse of a right triangle with the two given points as endpoints, and the two sides of the right triangle parallel to the x-axis and y-axis, respectively. The length of the segment parallel to the x-axis is the difference between the x-coordinates of the two points. The length of the segment parallel to the y-axis is the difference between the y-coordinates of the two points. Use the Pythagorean Theorem a^{2}+b^{2}=c^{2} or c=√(a^{2}+b^{2}) to find the distance. The formula is: “distance”=√((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}). To find the Midpoint of two points (x_{1},y_{1}) and (x_{2},y_{2}), average the x-coordinates to get the x-coordinate of the midpoint, and average the y-coordinates to get the y-coordinate of the midpoint. The formula is “midpoint”=((x_{1}+x_{2})/2,(y_{1}+y_{2})/2).

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Last updated: 02/19/2018

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