Question

Points B, O, Y are collinear on BY, and BO:OY=5/8. B is located at (4,2), O is located at (7, -3) and Y is located at (x,y). Determine the values x and y

Answer 1

x =
`(59)/(5)`

y = -11

Step-by-step explanation:

Given that a line segment BY. O is the point lies between B & Y.

Ratio is BO:OY = 5:8

Coordinate of point B = (4,2)

Coordinate of point O = (7,-3)

We will find the coordinate of Y (x,y)

Here we use the section formula.

Internal section formula is :

`Y(x,y) =((mx_(2)+nx_(1))/(m + n),(my_(2)+ny_(1))/(m + n))`

(7,-3) =
`((5*x+8*4)/(5+8) ,(5*y+8*2)/(5+8) )`

(7,-3) =
`((5x+32)/(13), (5y+16)/(13))`

Now

7 =
`(5x+32)/(13)`

5x+32 = 91

x =
`(59)/(5)`

and

`-3 =(5y+16)/(13)`

5y + 16 = -39

y = -11

That's the final answer.