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. Explai

Question

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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. Explai

n 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.

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-04-06T01:17:32+03:00

1. According to the definition, a specific point that splits a line segment into a ratio of a:b is indicated by the following x-coordinate:

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

And the y-coordinate:

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

2. Keeping this in 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: $L(2,0)$