Question

What are the coordinates of the point on the directed line segment from (-10, -3)

to (2, -3) that partitions the segment into a ratio of 5 to 3?

Answer 1

(-2.5,-3)

Explanation:

Initial points,
`(x_1,y_1)=(-10,-3)`

Final points,
`(x_2,y_2)=(2,-3)`

The ratio in which the points divides is 5:3. KLet (x,y) be the coordinates of the point that is directed on the line segment from (-10, -3) to (2, -3).

Using section formula,

`x=(m_1x_2+m_2x_1)/(m_1+m_2), y=(m_1y_2+m_2y_1)/(m_1+m_2)\\\\x=(5* 2+3* (-10))/(5+3), (5(-3)+3(-3))/(5+3)\\\\x=-2.5, y=-3`

So, the coordinates of the point is (-2.5,-3).