Question

Point A is located at (4, 9) and point B is located at (12,−5) .

What are the coordinates of the point that partitions the directed line segment AB⎯⎯⎯⎯⎯ in a 1:3 ratio?



Enter your answer, as decimals, in the boxes.

Answer 1

use the formula: x=x1+k(x2-x1), y=y1+k(y2-y1), k is the ratio of the first segment to the whole line segment. in this case, k=1/4
so x=[4+1/4(12-4)]=6
y=[9+1/4(-5-9)]=5.5
so the answer is (6, 5.5)

Answer 2

The coordinates of the point that partitions the directed line segment AB in a 1:3 ratio is (6,5.5)

What is a line segment ?

A line which has two end points and a fixed measurement is called a line segment.

It is given that Point A is located at (4, 9) and point B is located at (12,−5)

(x,y)= tA+(1-t)B

with the endpoint A at t=0 and B at t=1.

If the segment has to be partitioned such that BX=3AX, i.e. closer to A. That’s a  bigger than a half, so it’s

t=3/(3+1)=3/4

$\rm X = \dfrac {3}{4} (4,9) + \dfrac {1}{4} (12,-5)\\\\X = (6 , 5.5)$

the coordinates of the point that partitions the directed line segment AB in a 1:3 ratio is (6,5.5).

To know more about Line segment

https://brainly.com/question/25727583

#SPJ2