Question

How do you find the midpoint of `(5 1/2, -4 1/4), (3 3/4, -1 1/4)`?

Answer 1

See the full process for finding the midpoint below:

Explanation:

First, convert all of the mixed fractions to improper fractions over the same common denominator:

`(((4/4xx5) + (2/2 xx 1/2))`, `((4/4 xx -4) - 1/4))` and

`(((4/4 xx 3) + 3/4)`, `((4/4 xx -1) - 1/4))`

`((20/4 + 2/4)`, `(-16/4 - 1/4))` and

`((12/4 + 3/4)`, `(-4/4 - 1/4))`

`(22/4`, `-17/4)` and `(15/4`, `-5/4)`

We can now use the midpoint formula to find the midpoint of these two points.

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 points from our problem gives:

`M = ((color(red)(22/4) + color(blue)(15/4))/2 , (color(red)(-17/4) + color(blue)(-5/4))/2)`

`M = ((37/4)/2 , (-22/4)/2)`

`M = (37/8 , -22/8)`

`M = (4 5/8, -2 6/8)`

`M = (4 5/8, -2 3/4)`