Question

What are the coordinates of the point on the directed line segment from (-10, -1)(−10,−1) to (10, -6)(10,−6) that partitions the segment into a ratio of 3 to 2?

Answer 1

Answer:

Therefore,

The Coordinates of the point on the directed line segment from (-10, -1) to (10,−6) that partitions the segment into a ratio of 3 to 2 is

$P(x,y)=(2,-4)$

Step-by-step explanation:

Given:

Let Point P ( x , y ) divides Segment AB in the ratio 3 : 2 = m : n (say)

point A( x₁ , y₁) ≡ ( -10 , -1)  

point B( x₂ , y₂) ≡ ( 10 , -6)  

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

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

Substituting the values we get

$P(x,y)=(\dfrac{(3\times 10 +2\times -10) }{(3+2)},\dfrac{(3\times -6 +2\times -1) }{(3+2)})$

$P(x,y)=(\dfrac{10}{5},\dfrac{-20) }{5})$

$P(x,y)=(2,-4)$

Therefore,

The Coordinates of the point on the directed line segment from (-10, -1) to (10,−6) that partitions the segment into a ratio of 3 to 2 is

$P(x,y)=(2,-4)$