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)=( (m+k)/(2) , (n+l)/(2))`,



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

the midpoint is


`( (a+(-3a))/(2) , (2b+4b)/(2) )=( (-2a)/(2) , (6b)/(2) )=(-a, 3b)`


Answer: (-a, 3b)