Question

2. Find the coordinates of P so that P partitions AB in the ratio 5.1 with A(2, 4) and B(8, 10).

Answer 1

The coordinates of P is;

`P=(7,9)`

Step-by-step explanation:

We want to find the coordinate of P such that P partitions AB in the ratio 5:1.

Given the coordinates of A and B as;

`\begin{gathered} A(2,4) \\ B(8,10) \end{gathered}`

Let (x,y) represent the coordinates of point P;

`\begin{gathered} (x-2)/(8-x)=(5)/(1) \\ x-2=5(8-x) \\ x-2=40-5x \\ x+5x=40+2 \\ 6x=42 \\ x=(42)/(6) \\ x=7 \end{gathered}`
`\begin{gathered} (y-4)/(10-y)=(5)/(1) \\ y-4=5(10-y) \\ y-4=50-5y \\ y+5y=50+4 \\ 6y=54 \\ y=(54)/(6) \\ y=9 \end{gathered}`

Therefore, the coordinates of P is;

`P=(7,9)`