Question

What are the coordinates of the point on the directed line segment from ( − 10 , 2 ) (−10,2) to ( − 10 , − 5 ) (−10,−5) that partitions the segment into a ratio of 6 to 1?

Answer 1

Answer: $(-10,-4)$

Step-by-step explanation:

Given

The points joining line segment are (-10,2) and (-10,-5)

Using section formula, a point joining segment  $(x_1,y_1)\ \text{and}\ (x_2,y_2)$ divides it in k:1  has coordinates

$x=\dfrac{kx_2+1\cdot x_1}{k+1}$, $y=\dfrac{ky_2+y_1}{k+1}$

Ratio is 6:1

Coordinates are

$\Rightarrow x=\dfrac{6(-10)+(-10)}{6+1}\\\\\Rightarrow x=-10$

$\Rightarrow y=\dfrac{-5(6)+1(2)}{6+1}\\\\\Rightarrow y=\dfrac{-28}{7}\\\\\Rightarrow y=-4$

Thus, the coordinates are $(-10,-4)$