Question

The coordinates of points A and B are A(2,3).B(4,-5).M is the midpoint of vector AB.Determine the coordinates of point M and the magnitude of vector BM.

Answer 1

M is the average of A and B (both x and y).
That is, M = (A+B)/2
so also |BM| = 1/2 |AB| since length is a linear function
(you can use the distance formula, and show that 1/2 factors out)

Answer 2

A(2, 3), M(x, y), B(4, -5).
AM = AB/2
x-2 = (4-2)/2
X = 3.

y-3 = (-5-3)/2
Y =