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

Answer:

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

Step-by-step 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:

                                            $\left(\frac{m\:x_2+n\:x_1}{m+n},\:\frac{m\:y_2+n\:y_1}{m+n}\right)$

Here,

• x₁ = 2
• y₁ = 2

• x₂ = 7

• y₂ = 17

• $m=3,\:n=2$

Substituting the values in the above formula

$D\left(x\right)=\left(\frac{3\times \:7\:+\:2\times 2}{3+2},\:\frac{3\times 17\:+\:2\times 2}{3+2}\right)$

$D\left(x\right)=\left(\frac{21\:+\:4}{5},\:\frac{51\:+\:4}{5}\right)$

$D\left(x\right)=\left(\frac{25}{5},\:\frac{55}{5}\right)$

As

$\frac{25}{5}=5,\:\frac{55}{5}=11$

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).