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

Answer:

x = $\frac{59}{5}  $

y = -11

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) =(\frac{mx_{2}+nx_{1}}{m + n},\frac{my_{2}+ny_{1}}{m + n})  $

(7,-3) =$ (\frac{5*x+8*4}{5+8} ,\frac{5*y+8*2}{5+8} )  $

(7,-3) = $ (\frac{5x+32}{13}, \frac{5y+16}{13})  $

Now

7  = $\frac{5x+32}{13}  $  

5x+32 = 91

x = $\frac{59}{5}  $

and

$-3 =\frac{5y+16}{13}  $

5y + 16 = -39

y = -11

That's the final answer.