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 would approach this by first finding the equation of the line that goes through the two points. Then determine the distance between X and Y. Once you know the distance you can find the lengths of the two partitions according to the ratio of 4:1.

Answer 2

so the distance formula gives me 9/5

Answer 3

so if you divide 9 by 5 you get 1.8 then if you multiply that by 4 you get 7.2 which would be the distance between X and M and then the remaining 1.8 would be the distance between Y and M

Answer 4

so i think that would make M (8.2 , 2)

Answer 5

@luffingsails O.K. give us a further hint. We can use the distance formula to find the distance between X and Y. \[\sqrt{(1 - 10)^{2}+ (-2 - 3)^{2}} =\sqrt{106}= 10.3\] or the equation of line XY is slope being 5/9 or Y = (5X)/9 - 23/9. The problem requires us to find the point M.
M(x,y)

Answer 6

@Superwholock221 We can verify your answer to determine if it is correct. First lets find the distance XM using your values.\[D=\sqrt{(1 - 8.2)^{2}+(-2-2)^{2}}=\sqrt{51.84+16}=\sqrt{67.84}=8.24\]According to the problem the distance MY would be 1/4 of that or 2.06 and their sum should equal to the line distance XY. They add up to 10.3. Looks close enough to me.