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?

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

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

Substituting the values we get

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

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47