Question

What are the coordinates of the point on the directed line segment from (-4, - 7) to

(-3,1) that partitions the segment into a ratio of 2 to 3?

Answer 1

The coordinates of the point on the directed line segment from (-4, - 7) to

(-3,1) that partitions the segment into a ratio of 2 to 3 is

`\therefore P(x,y)=((-18)/(5),(-19)/(5))`

or

∴ PointP( x , y ) = ( -3.6, -3.8)

Explanation:

Let he points be,

point A( x₁ , y₁) ≡ ( -4 ,-7)

point B( x₂ , y₂) ≡ (-3 , 1)

and Point P( x , y ) be the point on the line Segment AB Divides AB internally in the ratio 2 : 3 i. e m : n

To Find:

Point P( x , y ) = ?

Solution:

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

`x=((mx_(2) +nx_(1)) )/((m+n))\\ \\and\\\\y=((my_(2) +ny_(1)) )/((m+n))\\\\`

Substituting the Given values we get

`x=((2(-3) +3(-4)) )/((2+3))\\ \\and\\\\y=((2(1) +3(-7)) )/((2+3))\\\\x=(-18)/(5)\\ \\and\\\\y=(-19)/(5)\\\\\therefore P(x,y)=((-18)/(5),(-19)/(5))`

∴ PointP( x , y ) = ( -3.6, -3.8)