Question

Oint A is located at (2, 6) and point B is located at (18, 12).

What point partitions the directed line segment ​ AB¯¯¯¯¯ ​ into a 2:3 ratio?
825, 825)

(1012, 1012)

(1139, 935)

(1412, 12)

Answer 1

`((42)/(5),(42)/(5))`

Explanation:

We are given that

Point A is at (2,6) and point B is at (18,12).

We have to find the point which partitions the directed line segment AB into a ratio 2:3.

We have
`x_1=2, y_1=6,x_2=18,y_2=12,m_1=2,m_2=3`

Section formula:
`x=(m_1x_1+m_2x_2)/(m_1+m_2), y=(m_1y_1+m_2y_2)/(m_1+m_2)`

Substitute the values in the given formula then, we get

The coordinates of point which partitions the segment AB is given by

`x=(2(18)+3(2))/(2+3), y=(2(12)+3(6))/(2+3)`

`x=(36+6)/(5),y=(24+18)/(5)`

`x=(42)/(5), y=(42)/(5)`

Hence, the coordinated of the point which partitions the line segment AB =
`((42)/(5),(42)/(5))`

Answer 2

Answer:(8 2/5, 8 2/5)

Explanation: