Question

Given directed line segment KM , find the coordinates of L such that the ratio

Answer 1

Answer:

The answer is below

Explanation:

The question is not complete, the coordinates of K and M are not given. Let us assume The coordinates are at K(1, -6) and M(9,-2)  

Answer: If a line segment AB with coordinates at $(x_1,y_1)\ and\ (x_2,y_2)$ is divided by a point O(x, y) in the ratio n:m, the coordinates of point O is given by the formula:

$x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1$

K(1, -6) and M(9,-2)  are divided in ratio 1:3 by point L. Let us assume L is at (x,y), hence the coordinate of point L is given as:

$x=\frac{n}{n+m}(x_2-x_1)+x_1=\frac{1}{1+3}(9-1)+1=\frac{1}{4}(8)+1=3 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1=\frac{1}{1+3}(-2-(-6))+(-6)=\frac{1}{4} (4)-6=-5$

Point L is at (3, -5)