Question

Find the distance between the two points andthe midpoint of the line segment joining thepoints.

Answer 1

The distance, d, between two points (x1, y1) and (x2, y2) is calculated as follows:

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

Substituting with points (5/2, -1) and (-3/2, 4), we get:

`\begin{gathered} d=\sqrt[]{(-(3)/(2)-(5)/(2))^2+(4-(-1))^2} \\ d=\sqrt[]{(-4)^2+5^2} \\ d=\sqrt[]{16+25} \\ d=\sqrt[]{41} \\ d\approx6.4 \end{gathered}`

The coordinates of the midpoint between two points (xm, ym) are computed as follows:

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

Substituting with points (5/2, -1) and (-3/2, 4), we get:

`\begin{gathered} (x_m,y_m)=(((5)/(2)-(3)/(2))/(2),(-1+4)/(2)) \\ (x_m,y_m)=((1)/(2),(3)/(2)) \end{gathered}`