Question

Point m is the midpoint of line segment ab, b is at (20,4), m is at (18, -2) and a is at (p,q). what is p+q?

Answer 1

The x-value of a midpoint is the average of the x-values of the ends.
The y-value of a midpoint is the average of the y-values of the ends.

The x-value of the end at b is 20 and it's 18 at the middle.
x has decreased by 2 in the course of 1/2 of the line.
So it will decrease another 2 during the other half of the line.
The x-value at the other end, at a, then, is 16.

The y-value of the end at b is 4 and it's -2 at the middle.
y has decreased by 6 in the course of 1/2 of the line.
So it will decrease another 6 during the other half of the line.
The y-value at the other end, at a, then, is -8.

The other end of the line, at a, is at  (16, -8) .

The sum of the coordinates at a (p+q) is  8  .