Question

A segment has endpoints with coordinates (a,2b) and (-3a,4b). write the coordinates of the midpoint of the segment in terms of a and b

Answer 1

Given any 2 point P(m,n) and Q(k,l),

the coordinates of the midpoint of the line segment PQ are given by the formula:

$M_{PQ}=( \frac{m+k}{2} , \frac{n+l}{2})$, 



Thus, given the points with coordinates (a,2b) and (-3a,4b), 

the midpoint is 

$( \frac{a+(-3a)}{2} , \frac{2b+4b}{2} )=( \frac{-2a}{2} , \frac{6b}{2} )=(-a, 3b)$


Answer: (-a, 3b)