Question

Find the coordinates of the midpoint M and the distance between (-5, 6) and (3, 2).Round to the nearest tenth if necessary.The coordinates of the midpoint M are____The distance between the two points is about ____See image for more clear

Answer 1

Explanation

We are given the following points:

`\begin{gathered} (-5,6) \\ (3,2) \end{gathered}`

We are required to determine the midpoint M and the distance between the given points.

We know that the midpoint of two points is given as:

`Midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2))`
`\begin{gathered} (-5,6)\to(x_1,y_1) \\ (3,2)\to(x_2,y_2) \\ M=((-5+3)/(2),(6+2)/(2))=((-2)/(2),(8)/(2)) \\ M=(-1,4) \end{gathered}`

Hence, the midpoint is:

`M=(-1,4)`

Also, the distance between two points is given as:

`Distance=√((y_2-y_1)^2+(x_2-x_1)^2)`
`\begin{gathered} (-5,6)\to(x_1,y_1) \\ (3,2)\to(x_2,y_2) \\ Distance=√((2-6)^2+(3-(-5))^2) \\ Distance=√((-4)^2+(3+5)^2)=√(16+64) \\ Distance=√(80)=4√(5)\text{ }units \end{gathered}`

Hence, the distance is:

`D=4√(5)\text{ }units`