Question

The endpoints of AB⎯⎯⎯⎯⎯ are A(1, 4) and B(5, -1). What are the coordinates of the point that divides AB⎯⎯⎯⎯⎯ in the ratio 2 : 3?

Answer 1

this is the way I do the question

\[\frac{2}{3} = \frac{A}{B}\]

cross multiply

2B = 3A

so then is

2(5, -1) = 3(1, 4)

so for x

\[x = \frac{2 \times 5 + 3 \times 1}{2 + 3}\]

and \[y = \frac{2 \times -1+ 3 \times 4}{2 + 3}\]

now just simplify them...