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Marat540 [252]
3 years ago
12

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

Mathematics
1 answer:
Elden [556K]3 years ago
6 0

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.

<u>SECTION FORMULA</u>

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).

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