Question

A classmate tells you "Finding the coordinates of the midpoint is easy. You must just find the averages." Is there any truth to it? Explain what you think your classmate means.

Answer 1

yes, that's true. the coordinates of the midpoint is the average of the coordinates of the endpoints.
If \((x_1,y_1)\) and \((x_2,y_2)\) are endpoints, the midpoint is
\[\left( \frac{ x_1+x_2 }{ 2 },\frac{ y_1+y_2 }{ 2 } \right)\]

Answer 2

it can be seen that the midpoint is the 'middle' of both the x and y lines

now:

the length of the Y dotted line is x2-x1

and the length of half of this is therefore

(x2-x1) / 2

but you need to add the start point to this to get the actual midpoint

so midpoint = (x2-x1)/2 + x1

and that is the same as (x1+x2)/2

which is the same as the average of x1 and x2

same for Y