Question

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

Answer 1

Answer:

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

$\therefore P(x,y)=(\frac{-18}{5},\frac{-19}{5})$

or

∴ PointP( x , y ) = ( -3.6, -3.8)

Step-by-step 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

$x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}$

Substituting the Given values we get

$x=\frac{(2(-3) +3(-4)) }{(2+3)}\\ \\and\\\\y=\frac{(2(1) +3(-7)) }{(2+3)}\\\\x=\frac{-18}{5}\\ \\and\\\\y=\frac{-19}{5}\\\\\therefore P(x,y)=(\frac{-18}{5},\frac{-19}{5})$

∴ PointP( x , y ) = ( -3.6, -3.8)