Question

Find the midpoint of the line segment connecting the points (-2, 4) and (2, - 8).

Then find the distance between the points.

Answer 1

see explanation

Explanation:

the midpoint (M) of a segment is the average of the x and y coordinates of the 2 points

M = (
`(x_(1)+x_(2) )/(2)` ,
`(y_(1)+y_(2) )/(2)` )

let (x₁, y₁ ) = (- 2, 4 ) and (x₂, y₂ ) = (2, - 8 )

substitute these values into the formula for M

M = (
`(-2+2)/(2)` ,
`(4-8)/(2)` ) = (
`(0)/(2)` ,
`(-4)/(2)` ) = (0, - 2 )

calculate the distance, d , between the 2 points using the distance formula

d =
`\sqrt{(x_(2)-x_(1) } )^2+(y_(2)-y_(1))^2`

let (x₁, y₁ ) = (- 2, 4 ) and (x₂, y₂ ) = (2, - 8 )

substitute these values into the formula for d

d =
`√((2-(-2))^2+(-8-4)^2)`

=
`√((2+2)^2+(-12)^2)`

=
`√(4^2+144)`

=
`√(16+144)`

=
`√(160)`

≈ 12.6 units ( to the nearest tenth )