Question

point M on a segment with endpoints X (1, −2) and Y (10, 3) partitions the segment in a 5:1 ratio. Find M. You must show all work to receive credit.

Answer 1

help pls

Answer 2

@tetsxpreme

Answer 3

If a segment needs to be split into a 5:1 ratio, then essentially you split it into 6 equal parts, and so one side has 1 part, the other has 5 parts.

So first, use the pythagorean theorem to find the distance between the two points.

Answer 4

how do i use the pythagorean theorem

Answer 5

a^2 + b^2 = c^2
a is the change in x, b is the change in y

Answer 6

sorry i just dont understand

Answer 7

Since XM: MY = 5 : 1, to find the point M you need to add 5 parts out of 5 + 1 = 6 parts
of the difference of the end points of the segment XY.
Use the formula below to find coordinates of point M:
x = 1 + 5/6(10 - 1)
y = - 2 + 5/6(3 - (-2))

Answer 8

let the coordinates of M be (x,y)
if M divides A(x1,y1) and B(x2,y2) in the ratio m:n then
\[x=\frac{ mx2+nx1 }{ m+n },y=\frac{ my2+ny1 }{ m+n}\]
\[x=\frac{ 5\times 10+1\times 1}{ 5+1}=\frac{ 50+1 }{ 6 }=\frac{ 51 }{ 6 }=\frac{ 17 }{ 2 }\]
\[y=\frac{ 5\times3+1\times -2 }{ 5+1}=\frac{ 15-2 }{ 6 }=\frac{ 13 }{ 6 }\]
so coordinates of M are \[(\frac{ 17 }{ 2 },\frac{ 13 }{ 6})\]