Question

Point P lies on the directed line segment from A(2,3) to B(8,0) and ​partitions the segment in the ratio 22 to 11. ​ ​What are the coordinates of ​point P ?

Answer 1

The coordinates of point P is 6 , 1

Explanation:

Given as :

The point P lies on directed line segment from points A and B

A = (
`x_1` ,
`y_1` ) = (2 ,3)

B = (
`x_2` ,
`y_2` ) = (8 , 0)

The partitions segments in the ratio = m : n = 22 : 11

Let the coordinate of point P = x , y

Now, According to question

x =
`(m* x_2 + n* x_1)/(m + n)`

y =
`(m* y_2 + n* y_1)/(m + n)`

Now

x =
`(m* x_2 + n* x_1)/(m + n)`

Or, x =
`(22* 8 + 11* 2)/(22 + 11)`

Or, x =
`(176 + 22)/(33)`

Or, x =
`(198)/(33)`

∴ x = 6

Again

y =
`(m* y_2 + n* y_1)/(m + n)`

Or, y =
`(22* 0 + 11* 3)/(22 + 11)`

Or, y =
`(0 + 33)/(33)`

Or, y =
`(33)/(33)`

∴ y = 1

So, The coordinates of point P = x , y = 6 , 1

Hence, The coordinates of point P is 6 , 1 Answer