Question

Find the point, M, that divides segment AB into a ratio of 5:5 if A is at (0, 15) and B is at (20,0).

Answer 1

The point M is (10,7.5).

Explanation:

Given:

AB is in a ratio of 5:5. A is at (0, 15) and B is at (20,0).

Now, to find the point M that divides the segment AB.

The points are A (0,15) and B (20,0) of the segment AB, which divides the point into
`m_(1)andm_(2)` .

So,
`m_(1)=5,m_(2)=5`.

`A= (x_(1),y_(1) )(0,15)` and
`B=(x_(2),y_(2))(20,0)`

So, by putting the formula to find M.

`x= \frac{m_(1) x_(2)+m_(2)x_(1)} {m_1+m_2}`

`x= (5* 20+5* 0)/(5+5)`

`x= (100)/(10)`

`x=10`

`y= \frac{m_(1) y_(2)+m_(2)y_(1)} {m_1+m_2}`

`y= (5* 0+5* 15)/(5+5)`

`y= (75)/(10)`

`y=7.5`

So, the required point is
`(x,y)`=(10,7.5)

Therefore, the point M is (10,7.5).