Question

Using the image below, find the point that divides the line segment AB into a ratio of 2:3.

Answer 1

The point of division 2/3 is given by:
xm=xa+(xb-xa)*2/3
ym=ya+(yb-ya)*2/3

Answer 2

From the diagram, the coordinates of A are (-4,6), so xa=-4, ya=6.
B(5,1), so xb=5, yb=1.
The formula I gave is the standard point of division formula, where
xm, ym are the x- and y-coordinates of the required point which divides AB in ratio 2/3.
Oops, the formulas should read:
xm=xa+(xb-xa)*2/5
ym=ya+(yb-ya)*2/5
because 5=2+3

Answer 3

So is my answer (0.5, 3.5) ?

Answer 4

@mathmate

Answer 5

not quite, but close.
Did you do
xm=-4+(5-(-4))*2/5
ym=6+(1-6)*2/5
or did you use a different formula?