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. You must show all work to receive credit.

Answer 1

Answer:

$\displaystyle \: M = \left( 8\frac{1}{5},2\right)$

Step-by-step explanation:

we want to figure out the point "M" which is on a segment with endpoints X(1,-2) and Y(10,3) partitions the segment in a 4:1 ratio.

to find so, we can consider section formula . we know that Section formula is used to find the ratio in which a line segment is divided by a point internally or externally the ratio is written as m:n

however in this case the following formula can be used used:

$\displaystyle \left( \frac{m x_{2} +n x_{1}}{m + n} , \frac{m y_{2} + n y_{1}}{m +n}\right)$

step-1: assign variables

assign variables:

• $(x_{1},y_{1}) = (1, - 2)$
• $(x_{2},y_{2}) = (10, 3)$
• $m : n = 4 :1$

step-2: substitute

$\displaystyle \left( \frac{(4) (10) +(1)(1) }{4 +1} , \frac{(4)(3)+ (1) ( - 2)}{4 +1}\right)$

simplify multiplication:

$\displaystyle \left( \frac{40 + 1 }{4 + 1} , \frac{12+ ( - 2)}{4 + 1}\right)$

simplify addition:

$\displaystyle \left( \frac{41 }{5} , \frac{10}{5}\right)$

simplify division:

$\displaystyle \left( 8\frac{1}{5},2\right)$

hence,

$\displaystyle \: M = \left( 8\frac{1}{5},2\right)$

Answer 2

9514 1404 393

Answer:

  M = (8.2, 2)

Step-by-step explanation:

We want ...

  XM/MY = 4/1

  XM = 4MY

  M -X = 4(Y -M) . . . . . . the length of AB is B-A for this purpose

  M +4M = 4Y +X . . . . . add 4M+X

  M = (4Y +X)/5 . . . . . . .divide by 5

  M = (4(10, 3) +(1, -2))/5 = (40+1, 12-2)/5 = (41/5, 10/5)

  M = (8.2, 2)