Question

Find the point that partitions line segment AB with

endpoints A(-2, 1) and B(4,6) in a ratio of 1:2.

Answer 1

The coordinates of
`(x,y)  = (0,(8)/(3) )`

Explanation:

The coordinates of the points are given as A(-2, 1) and B(4,6).

The ratio is 1 : 2

Le t us assume the point is M (x,y).

⇒ AM : MB = 1 : 2

Now, Using SECTION FORMULA:

`(x,y)  = ((m1 x2 + m2 x1)/(m1 + m2) ,(m1 y2 + m2 y1)/(m1 + m2))`

Using m1 : m2 = 1 : 2

Here, we get

`(x,y)  = ((1(4)  + 2(-2))/(1 + 2) ,(1(6) + 2(1))/(1 + 2))\\\implies (x,y) = ((4-4)/(3) ,(6+2)/(3) )\\or, (x,y) = (0 ,(8)/(3) )`

Hence, the coordinates of
`(x,y)  = (0, (8)/(3) )`