Question

What are the coordinates of the point on the directed line segment from (-9, -1)(−9,−1) to (-9, -10)(−9,−10) that partitions the segment into a ratio of 2 to 1?

Answer 1

Answer:

Therefore the co-ordinate of the point on the line segment from (-9,-1) to(-9,-10) into a ratio internally is (-9,-7).

Therefore the co-ordinate of the point on the line segment from (-9,-1) to(-9,-10) into a ratio internally is (-9,-19).

Step-by-step explanation:

Given points are (-9,-1) and (-9,-10)

If a point divides the line segment by joining two points (x₁,y₁) and (x₂,y₂)  into a ratio m:n internally.

Then the point of the coordinate is $(\frac{m.x_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$.

If a line segment is externally divided into a point by joining two points (x₁,y₁) and (x₂,y₂) with m: n ratio.

Then the point of the coordinate is $(\frac{m.x_2-nx_1}{m-n},\frac{my_2-ny_1}{m-n})$.

Internally

The co-ordinate of the point is $(\frac{(-9)\times2+(-9)\times 1}{2+1},\frac{(-10)\times 2+(-1)\times 1}{2+1})$

                                                 $=(-9,-7)$

Externally

The co-ordinate of the point is $(\frac{(-9)\times2-(-9)\times 1}{2-1},\frac{(-10)\times 2-(-1)\times 1}{2-1})$

                                                   =  (-9,-19)