Question

How do you find the midpoint of (-5, 4) and (3, 2)?

Answer 1

See the solution process below:

Explanation:

The formula to find the mid-point of a line segment give the two end points is:

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

Where `M` is the midpoint and the given points are:

`(color(red)((x_1, y_1)))` and `(color(blue)((x_2, y_2)))`

Substituting the values from the points in the problem gives:

`M = ((color(red)(-5) + color(blue)(3))/2 , (color(red)(4) + color(blue)(2))/2)`

`M = (-2/2 , 6/2)`

`M = (-1, 3)`

Answer 2

Use the formulas:
`x_"midpoint"=(x_"start"+x_"end")/2`
`y_"midpoint"=(y_"start"+y_"end")/2`

Explanation:

Given the start point `(-5,4)` and the end point `(3,2)`:

`x_"midpoint"=(-5+3)/2 = (-2)/2 = -1`
`y_"midpoint"=(4+2)/2= 6/2 = 3`

The midpoint is: `(-1,3)`