Question

Find the coordinates of point P that partition AB in the

ratio 1:4.

Please give explanation

Answer 1

(1.6, 0)

Explanation:

Point P, partitioning AB in the ratio 1:4, implies that it divides AB into, AP and PB, such that AP to PB = 1:4.

Use the formuka below to find the coordinates of point P:

`x = (mx_2 + nx_1)/(m + n)`

`y = (my_2 + ny_1)/(m + n)`

Where,

`A(1, -1) = (x_1, y_1)`

`B(4, 4) = (x_2, y_2)`

`m = 1, n = 4`

Solve by plugging the above values where necessary as follows:

`x = (mx_2 + nx_1)/(m + n)`

`x = (1(4) + 4(1))/(1 + 4)`

`x = (4 + 4)/(5)`

`x = (8)/(5)`

`x = 1.6`

`y = (my_2 + ny_1)/(m + n)`

`y = (1(4) + 4(-1))/(1 + 4)`

`y = (4 - 4)/(5)`

`y = (0)/(5)`

`y = 0`

The coordinates of P that partitions AB into the ratio 1:4 are (1.6, 0)