Question

4. Point P is located at (2, 2) and point T is located at (7, 17).

What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
Use the section formula and show values for: m: n, Point 1, Point 2, and ALL work to find coordinates of partitioning point.

Answer 1

The coordinates of the point that partitions PT is (5, 11).

Solution:

Given P(2, 2) and T(7, 17).

Line segment PT is divided the coordinates of the point in the ratio 3 : 2.

Let R be the divided point the line segment PT.

Section Formula:

The point (x, y) which divides the line segment of the points
`(x_1,y_1)` and
`(x_2,y_2)` in the ratio m : n is

`$\left((m x_(2) + n x_(1))/(m + n), (m y_(2) + n y_(1))/(m + n)\right)`

Here
`x_1=2,y_1=2,x_2=7,y_2=17` and m = 3, n = 2

Substitute these in the given formula.

`$R(x)=\left((3* 7 + 2*2)/(3+2), (3*17 + 2*2)/(3+2)\right)`

`$R(x)=\left((21 + 4)/(5), (51 + 4)/(5)\right)`

`$R(x)=\left((25)/(5), (55)/(5)\right)`

`$R(x)=(5, 11)`

Hence the coordinates of the point that partitions PT is (5, 11).