Question

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 the directed line segment PT in a 3:2 ratio will be (5, 11).

Explanation:

Given the points

• P(2, 2) and T(7, 17)

What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?

Let D be the Divided point of the directed line segment PT.

SECTION FORMULA

The point (x, y) which partitions the line segment of the points (x₁, y₁) and

(x₂, y₂) in a ratio
`m:n` will be:

`\left((m\:x_2+n\:x_1)/(m+n),\:(m\:y_2+n\:y_1)/(m+n)\right)`

Here,

• x₁ = 2
• y₁ = 2

• x₂ = 7

• y₂ = 17

• 
  `m=3,\:n=2`

Substituting the values in the above formula

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

`D\left(x\right)=\left((21\:+\:4)/(5),\:(51\:+\:4)/(5)\right)`

`D\left(x\right)=\left((25)/(5),\:(55)/(5)\right)`

As

`(25)/(5)=5,\:(55)/(5)=11`

So

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

Therefore, the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio will be (5, 11).