Question

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

Answer 1

midpoint `-> (x,y) -> (3,-3)`

Explanation:

Suppose `x_1` is the starting point and `x_2` is the end point for the x axis. Thus the mid point would `1/2` the difference added to the start point. The same thing for the y-axis.
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Consider the x-axis:

Let `{x_1 ,x_2} -> {2,4}`

Difference is `4-2=2`

half way from `x_1 -> 2/2=1`

So the x-coordinate for `1/2` way between `x_1" and x_2` is:

`x_1+1 = 2+1 =3`

so `x_("midpoint")=3`
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In the same way:

`y_("midpoint")=y_1 + (y_2-y_1)/2 =-4 + ( (-2)-(-4))/2`

`y_("midpoint")=" "-4 +(-2+4)/2" " =" " -4 +1 " "=" " -3`
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so midpoint `-> (x,y) -> (3,-3)`