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What are the coordinates of the point on the directed line segment from (-7, 10) to
(-2,-5) that partitions the segment into a ratio of 2 to 3?

Sagot :

line segment from (-10,-3) to (1,7)
a ratio of 2 to 3 means that the line segment is divided into 5 equal pieces
let (x,y) be 2/5 of the way from (-10,-3) to (1,7)
what is the distance of the segment ?
use the distance formula to find the distance of the segment
√(11^2+10^2)=√221
-10 to 1 is 11 units, 2/5(11)=4.4
-3 to 7 is 10 units, 2/5(10)=4
-10+4.4=-5.6
-3+4=1
the point is (-5.6,1)
check:
find the distance from (-10,-3) to (-5.6,1)
find the distance from (-5.6,1) to (1,7)
these distances should add up to √221
first distance:√[(4.4^2)+4^2]=√35.36
second distance:√[(6.6^2)+6^2]=√79.56
√35.56+√79.56=√221
5.946+8.919=14.866
14.865≈14.866
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