Question

A point M on a segment with endpoints X(1, -2) and Y(10, 3) partitions the segment in a 4:1 ratio. Find M

Answer 1

I start this way

so M be the point that divides XY .... I'll assume internal division

so then \[\frac{XM}{MY} = \frac{4}{1}\]

cross multiply

\[XM = 4MY\]

so then the formula is

so then using the points X and Y

1(1, -2) and 4(10,3)

this way you get the right ratios with the right points

then its simply a case of

\[x = \frac{1 \times 1 + 4 \times 10}{4 + 1}`~~~~y = \frac{1 \times -2 + 4 \times 3}{4 + 1}\]

to find M(x, y)

hope it helps...

if the division is external, make 1 of the ratio values negative.

Answer 2

alright thanks alot