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atroni [7]
3 years ago
11

Find the coordinate that divides the directed line segment from A(-2,-4) to B(8,1) in the ratio of 2 to 3

Mathematics
1 answer:
zalisa [80]3 years ago
7 0
We have that
A(-2,-4)  B(8,1) <span>

let
M-------> </span><span>the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3

we know that

A--------------M----------------------B
        2                     3
distance AM is equal to (2/5) AB
</span>distance MB is equal to (3/5) AB
<span>so

step 1
find the x coordinate of point M
Mx=Ax+(2/5)*dABx
where
Mx is the x coordinate of point M
Ax is the x coordinate of point A
dABx is the distance AB in the x coordinate
Ax=-2
dABx=(8+2)=10
</span>Mx=-2+(2/5)*10-----> Mx=2

step 2
find the y coordinate of point M
My=Ay+(2/5)*dABy
where
My is the y coordinate of point M
Ay is the y coordinate of point A
dABy is the distance AB in the y coordinate
Ay=-4
dABy=(1+4)=5
Mx=-4+(2/5)*5-----> My=-2

the coordinates of point M is (2,-2)

see the attached figure

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