The point " $C$ " and " $D$ " are on the line segment joining $A (- 4, 7)$ and $B (5, 13)$ such that $A C = C D = D B$ . Then find coordinates of point $C$ and $D$ .

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Solution

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in the ratio $m : n$ is
$(x, y) = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$
Since, $C$ and $D$ are on $A B$ , $A (- 4, 7)$ and $B (5, 13)$
Such that $A C = C D = D B$
So, $C$ and $D$ are points of trisection of $A B$ .
$=> C = (\frac{- 4 (2) + (1) (5)}{3}, \frac{7 (2) + 13 (1)}{3}) C = (- 1, 9)$
And
$D = (\frac{- 4 (1) + 2 (5)}{3}, \frac{7 (1) + 13 (2)}{3}) D = (2, 11)$

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