Question

How are the formulas for calculating the length of a line segment and the midpointof a line segment, using the coordinates of the endpoints, the same? How are theydifferent?

Answer 1

The length of a line segment conecting points (x1, y1) and (x2, y2) is

`L=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

The formula for calculating the coordinates of a midpoint is

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

The formula for the length of the line segment and the midpoint are different in the following manner.

The formula for the length of the line segment gives you a length.

The formula for coordinates of the midpoint gives you an ordered pair, the location of a point.

The two formulas are similar in that they both use the coordinates of two points to find the quantities desired ( length and location).