Question

3. Find the coordinates of P so that P partitions the segment AB in the ratio 5:1 if A(2,4) and B(8,10).

Answer 1

Step 1: Problem

Find the coordinates of P so that P partitions the segment AB in the ratio 5:1 if A(2,4) and B(8,10).​

Step 2: Concept

Let coordate of p = (x , y )

5:1 = m: n

`\begin{gathered} x=\frac{mx_2+nx_1}{m\text{ + n}}_{} \\ y\text{ = }\frac{my_2+ny_1}{m\text{ + n}} \end{gathered}`

Step 3: Method

Given data

`\begin{gathered} m\text{ = 5} \\ n\text{ = 1} \\ x_1\text{ = 2} \\ y_1\text{ = 4} \\ x_2\text{ = 8} \\ y_2\text{ = 10} \end{gathered}`
`\begin{gathered} x\text{ = }\frac{mx_2+nx_1}{m\text{ + n}} \\ x\text{ = }\frac{5\text{ x 8 + 1 x 2}}{5\text{ + 1}} \\ =\text{ }\frac{40\text{ + 2}}{6} \\ =\text{ }(42)/(6) \\ =\text{ 7} \\ \end{gathered}`
`\begin{gathered} y\text{ = }\frac{my_2+ny_1}{m\text{ + n}} \\ y\text{ = }\frac{5\text{ x 10 + 1 x 4}}{5\text{ + 1}} \\ y\text{ }=\text{ }\frac{50\text{ + 4}}{6} \\ y\text{ = }(54)/(6) \\ y\text{ = 9} \end{gathered}`

Step 4: Final answer

The coordinates of P = (7,9)