Question

Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates (22,2), determine and state the coordinates of P.

Answer 1

The coordinates of P are (12, 2).

Solution:

Given data:

`(x_1, y_1)= A (4, 2)` and
`(x_2, y_2)=B(22, 2)`

P(x, y) is the point on the line segment AB.

AP : PB = m : n = 4 : 5.

That is m = 4 and n = 5.

Section formula:

`$P(x, y)=\left((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n)\right)`

`$P(x, y)=\left((4* 22 + 5* 4)/(4+5), (4* 2 + 5* 2)/(4+5)\right)`

`$P(x, y)=\left((88 + 20)/(9), (8+10)/(9)\right)`

`$P(x, y)=\left((108)/(9), (18)/(9)\right)`

P(x, y) = (12, 2)

Hence the coordinates of P are (12, 2).