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:

$(\frac{m_1x_2+m_2x_1}{m_1+m_2} , \frac{m_1y_2+m_2y_1}{m_1+m_2})$

Here, $\frac{57}{8} = \frac{5x+(8 \times 4)}{5+8}$

$\frac{13 \times 57}{8} = 5x+32$

$\frac{741}{8} = 5x+32$

$5x= 60.625$

x = 12.125

Now, $-3=\frac{5y+(8 \times 2)}{5+8}$

$-39 = 5y+16$

$-55 = 5y$

y = -11

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