Question

point b, o, and y are collinear on by, and bo:oy = 5/8. B is located at (4,2,) o is located at (57/8,-3) and Y is located at (x,y) determine the value of x and y

Answer 1

Given: BO : OY = 5:8. Coordinate B is located at (4,2,) ; O is located at (57/8,-3) and Y is located at (x,y).

We have to determine the coordinate Y.

We will use cross section formula which states:

The coordinates
`(x_1,y_1) , (x_2,y_2)` are divided in the ratio
`m_1 : m_2` by the Coordinate A. So, the coordinates of A are given by the formula:

`((m_1x_2+m_2x_1)/(m_1+m_2) , (m_1y_2+m_2y_1)/(m_1+m_2))`

Here,
`(57)/(8) = (5x+(8 * 4))/(5+8)`

`(13 * 57)/(8) = 5x+32`

`(741)/(8) = 5x+32`

`5x= 60.625`

x = 12.125

Now,
`-3=(5y+(8 * 2))/(5+8)`

`-39 = 5y+16`

`-55 = 5y`

y = -11

So, the coordinate is Y(12.125, -11).