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 [tex](x_1,y_1) , (x_2,y_2)[/tex] are divided in the ratio [tex]m_1 : m_2[/tex] by the Coordinate A. So, the coordinates of A are given by the formula:
[tex](\frac{m_1x_2+m_2x_1}{m_1+m_2} , \frac{m_1y_2+m_2y_1}{m_1+m_2})[/tex]
Here, [tex]\frac{57}{8} = \frac{5x+(8 \times 4)}{5+8}[/tex]
[tex]\frac{13 \times 57}{8} = 5x+32[/tex]
[tex]\frac{741}{8} = 5x+32[/tex]
[tex]5x= 60.625[/tex]
x = 12.125
Now, [tex]-3=\frac{5y+(8 \times 2)}{5+8}[/tex]
[tex]-39 = 5y+16[/tex]
[tex]-55 = 5y[/tex]
y = -11
So, the coordinate is Y(12.125, -11).
