Question

Point M divides AB such that AM:MB = 1:4. If A has coordinates (-4, 3) and B has coordinates (6, 8). What are the coordinates of M?

Answer 1

Coordinates of M =
`\left ( -2,4 \right )`

Explanation:

Given: AM:MB = 1:4, A has coordinates (-4, 3) and B has coordinates (6, 8)

To find: coordinates of M

Solution:

According to section formula, if M(x, y) divides line joining points
`A(x_1,y_1)\,,\,B(x_2,y_2)` in ratio
`m:n` then coordinates of point M are
`\left ( (mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n) \right )`

Put
`A(x_1,y_1)=(-4,3)\,,\,B(x_2,y_2)=(6,8)\,,\,m:n=1:4`

Therefore,

`(x,y)=\left ( (6-16)/(1+4),(8+12)/(1+4) \right )=\left ( -2,4 \right )`