The endpoints of directed line segment PQ have coordinates of P(-7,5) and Q(5,3). What are the coordinates of point A, on PQ, that divide PQ into a ratio of 1:3?

Question

asked Mar 18, 2021 194k views

1 Answer

SpencerPark · Answer 1 · 2021-03-22T09:20:14+0000

Correction

P(-7,-5)

Answer:

d(-4,-3)

Explanation:

-Given the coordinates of PQ as P(-7,5) and Q(5,3).

-The sum of the ratios is:

$\sum(ratios)=1+3\\\\=4$

Let d be the point that divide's the segment in the ratio 1:3

#The coordinates that divide the segment into a 1:3 ratio therefore has to be
(1)/(4)|PQ| from P.

#We determine the length of the x-axis coordinate:

$|PQ|_x=Q_x-P_x\\\\=5--7\\\\=12\\\\\therefore d_x=-7+(1)/(4)* 12\\\\=-4$

#We determine the length of the y-axis coordinate:

$|PQ|_y=Q_y-P_y\\\\=3--5\\\\=8\\\\\therefore d_y=-5+(1)/(4)* 8\\\\=-3$

Hence, the coordinates of point d is d(-4,-3)