Question

The endpoints of AB are A (-4,8) and B (12,-4). How do you find the coordinates of P if P lies on AB and is 3/8 the distance from A to B?

Answer 1

`(\frac{4}{11}, \frac{52}{11})`

Explanation:

Assuming the point `P` lies on the line AB such that

`PA:PB=3:8\equiv m:n`

point `P` internally divides the line AB with end points `A(-4, 8)\equiv(x_1, y_1)` & `B(12, -4)\equiv(x_2, y_2)`.

The coordinates of point `P` are given by internal division formula as follows

`(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})`

`\equiv(\frac{3\cdot 12+8(-4)}{3+8}, \frac{3(-4)+8(8)}{3+8})`

`\equiv(\frac{4}{11}, \frac{52}{11})`