MATH SOLVE

5 months ago

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

Accepted Solution

A:

we have that

A(-2,-4) B(8,1)

let

M-------> 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

distance MB is equal to (3/5) AB

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

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

A(-2,-4) B(8,1)

let

M-------> 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

distance MB is equal to (3/5) AB

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

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