Answer:
So, the coordinate of point A that divides the line segment PQ two-third of the way from P to Q is [tex](6, 8)[/tex].
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 ([tex](x, y)[/tex].
The coordinate of a point A, which divides the line segment PQ two-thirds of the way from P to Q is,
[tex]x= \frac{m\times8+n\times2}{(m+n)}[/tex] [using section formula]
[tex]= \frac{2\times8+1\times2}{(2+1)}[/tex]
[tex]=6[/tex]
[tex]y= \frac{m\times11+n\times2}{(m+n)}[/tex] [using section formula]
[tex]= \frac{2\times11+1\times2}{(2+1)}[/tex]
[tex]=8[/tex]
So, the coordinate of point A that divides the line segment PQ two-third of the way from P to Q is [tex](6, 8)[/tex].
