Question 139

The points A(3, -5) and B(-5, 4) are given. If C is a point such that $$\frac{AC}{CB} = 2$$, then the coordinates of C are

Solution

$$\frac{AC}{CB}=2\ or\ AC=2CB$$

Hence C divides AB in the ratio of 2:1

Using the proportionality theorem of coordinate geometry

$$x=\frac{2\times\ \left(-5\right)+1\times\ 3}{3}=-\frac{7}{3}$$

$$x=\frac{2\times\ \left(4\right)+1\times\ \left(-5\right)}{3}=1$$

Hence the coordinates are (7/3,1)

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