Question

Given H(0,3) and Y(-2,5), find the coordinates of the point which divides segment YH in the ratio 2:5?

Answer 1

Using the section formula if any point (x,y) divides the line joining the point

in the ratio m:n then.

Given:

Coordinate is (x,y) is:

So the coordinates of point is (-4/7 , 25/7)

Answer 2

Using the section formula if any point (x,y) divides the line joining the point

`\begin{gathered} (x_1,y_1)_{} \\ \text{and} \\ (x_2,y_2) \end{gathered}`

in the ratio m:n then.

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

Given:

`\begin{gathered} (x_1,y_1)=(0,3) \\ (x_2,y_2)=(-2,5) \\ m=2 \\ n=5 \end{gathered}`

Coordinate is (x,y) is:

`\begin{gathered} x=(mx_2+nx_1)/(m+n) \\ x=((2*-2)+(5*0))/(5+2) \\ x=(-4)/(7) \end{gathered}`
`\begin{gathered} y=(my_2+ny_1)/(m+n) \\ y=((2*5)+(5*3))/(5+2) \\ y=(10+15)/(7) \\ y=(25)/(7) \end{gathered}`

So the coordinates of point is (-4/7 , 25/7)