Question

Find the midpoint and distance on points (5,5) and (-1,3)

Answer 1

Given:

Two points (5, 5) and (-1, 3).

To find the midpoint and distance:

Using the midpoint formula,

`\begin{gathered} m=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ =((5-1)/(2),(5+3)/(2)) \\ =((4)/(2),(8)/(2)) \\ =(2,4) \end{gathered}`

Thus, the mid-point formula is (2, 4).

Using the distance formula,

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}} \\ =\sqrt[]{(-1-5)^2+(3-5)^2} \\ =\sqrt[]{(-6)^2+(-2)^2} \\ =\sqrt[]{36+4} \\ =\sqrt[]{40} \\ =2\sqrt[]{10}\text{ units} \end{gathered}`

Thus, the distance between the two points is,

`2\sqrt[]{10}units`