Question

Given P(2,2) and Q(8,11) what are the coordinates of the point that divides PQ two-thirds of the way from P to Q.

Answer 1

So, the coordinate of point A that divides the line segment PQ two-third of the way from P to Q is
`(6, 8)`.

Explanation:

Given that,

Coordinate of point P is (2, 2).

Coordinate of point Q is (8, 11).

Now,

we have to find the coordinate of point that divides PQ two-thirds of the way from P to Q.

Let, A is the point that divides PQ two-thirds of the way from P to Q whose coordinate is (
`(x, y)`.

The coordinate of a point A, which divides the line segment PQ two-thirds of the way from P to Q is,

`x= (m*8+n*2)/((m+n))` [using section formula]

`= (2*8+1*2)/((2+1))`

`=6`

`y= (m*11+n*2)/((m+n))` [using section formula]

`= (2*11+1*2)/((2+1))`

`=8`

So, the coordinate of point A that divides the line segment PQ two-third of the way from P to Q is
`(6, 8)`.