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

Answer:

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

Step-by-step 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,

$x= \frac{m\times8+n\times2}{(m+n)}$              [using section formula]

  $= \frac{2\times8+1\times2}{(2+1)}$

  $=6$

$y= \frac{m\times11+n\times2}{(m+n)}$             [using section formula]

  $= \frac{2\times11+1\times2}{(2+1)}$

   $=8$

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