Question

What are the coordinates of the point on the directed line segment from (-2, 9)(−2,9) to (-1, -4)(−1,−4) that partitions the segment into a ratio of 2 to 3?

Answer 1

Answer:

Therefore the coordinates of the point on the directed line segment from (-2, 9) to (-1, -4) that partitions the segment into a ratio of 2 to 3 is

$P(x,y)=(-\dfrac{8}{5},\dfrac{19}{5})$

Step-by-step explanation:

Given:

Let point P divides Segment AB in the ratio 2 : 3

point A( x₁ , y₁) ≡ ( -2 , 9 )  

point B( x₂ , y₂) ≡ ( -1 , -4 )

m : n = 2 : 3

To Find:

P( x, y ) = ?

Solution:

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

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

Substituting the values we get

$x=\dfrac{(2(-1) +3(-2))}{(2+3)}\\ \\and\\\\y=\dfrac{(2(-4) +3(9)) }{(2+3)}$

$x=\dfrac{-8}{5}\\ \\and\\\\y=\dfrac{19}{5}$

Therefore the coordinates of the point on the directed line segment from (-2, 9) to (-1, -4) that partitions the segment into a ratio of 2 to 3 is

$P(x,y)=(-\dfrac{8}{5},\dfrac{19}{5})$