Question

What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J

Answer 1

Answer:

$\left ( \frac{3x_2+5x_1}{8},\frac{3y_2+5y_1}{8} \right )$

Step-by-step explanation:

Given: P is Three-fifths the length of the line segment from K to J

To find: x- and y-coordinates of point P on the directed line segment from K to J

Solution:

Section formula:

Let point K and J be $(x_1,y_1)\,,\,(x_2,y_2)$ such that the point $p(x,y)$ divides KJ in ratio $m:n$

Then coordinates of point  P are given by $\left ( \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n} \right )$

Take $m:n=3:5$

So,

coordinates of point P = $\left ( \frac{3x_2+5x_1}{3+5},\frac{3y_2+5y_1}{3+5} \right )=\left ( \frac{3x_2+5x_1}{8},\frac{3y_2+5y_1}{8} \right )$