Question

A. Given directed line segment MN with M(-6,-2) and N(3,1), find point P that partitions the segment into a ratio of 1:2. Explain your reasoning. B. Given directed line segment JK with J(-1,6) and K(3,-2), find point L that partitions the segment into a ratio of 3:1. Explain your reasoning.

Answer 1

1. By definition, a given point that divides a segment into a ratio a:b, as the following x-coordinate:

$x1+\frac{a}{a+b} (x2-x1)$

And the y-coordinate:

$y1+\frac{a}{a+b}(y2-y1)$

2. Kepping this on mind, you have:

A) x-coordinate:

$-6+(\frac{1}{1+2}) (3+6)=-3$

y-coordinate:

$-2+(\frac{1}{1+2} )(1+2)=-1$

The answer is: $P(-3,-1)$

B) The x-coordinate is:

$-1+(\frac{3}{3+1} )(3+1)=2$

The y-coordinate is:

$6+(\frac{3}{3+1} )(-2-6)=0$

The answer is: $L(2,0)$