Question

Can someone please answer this I don’t understand!
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 X are (5, 11).

Solution:

Given points of the line segment are P(2, 2) and T(7, 17)  

Let X be the point that partitions the directed line segment PT in the ratio 3 : 2

Using section formula, we can find the coordinate of the point that partitions the line segment.

Section formula:

$X(x, y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)$

Here, $x_{1}=2, y_{1}=2, x_{2}=7, y_{2}=17$ and m = 3, n =2

Substitute these in the section formula,

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

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

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

           $=(5, 11)$

X(x, y) = (5, 11)

The coordinates of X are (5, 11).