Question

Find the value of the coordinates that are 3/5 of the way between the points located at (3,2) and (6,8)

Answer 1

Assume X(3,2) and Y(6,8).

Let Z be the point which is 3/5 of the way between XY. So,

`\begin{gathered} XZ=(3)/(5)XY \\ (XZ)/(XY)=(3)/(5) \\ (XY)/(XZ)=(5)/(3) \\ (XZ+ZY)/(XZ)=(5)/(3) \\ (ZY)/(XZ)=(5)/(3)-1 \\ =(2)/(3) \end{gathered}`

So point Z divide the line XY in ratio 3:2.

The coordinate of point P if it divide the line A(x_1,y_1) and B(x_2,y_2) in ratio m:n is,

`(x,y)=((nx_1+mx_2)/(m+n),(ny_1+my_2)/(m+n))`

Determine the coordinate of point the divide the line joining points (3,2) and (6,8) in 3:2 ratio.

`\begin{gathered} (x,y)=((2\cdot3+3\cdot6)/(3+2),(2\cdot2+3\cdot8)/(3+2)) \\ =((6+18)/(5),(4+24)/(5)) \\ =((24)/(5),(28)/(5)) \end{gathered}`

So value of coodinate is (24/5,28/5)