Question

What are the coordinates of the point on the directed line segment from (-6, -3)(−6,−3) to (-1, 7)(−1,7) that partitions the segment into a ratio of 3 to 2?

Answer 1

Answer:

(-3,3).

Step-by-step explanation:

The given points are (-6,-3) and (-1,7).

We need to find the coordinates of the point, which divides the line segment in 3:2.

Section formula: If a point divides a line in m:n, then the coordinates of point are

$\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Using this formula, we get

$\left(\dfrac{3(-1)+2(-6)}{3+2},\dfrac{3(7)+2(-3)}{3+2}\right)$

$\left(\dfrac{-3-12}{5},\dfrac{21-6}{5}\right)$

$\left(\dfrac{-15}{5},\dfrac{15}{5}\right)$

$\left(-3,3\right)$

Therefore, the coordinates of required point are (-3,3).