Question

A(0,1) and B(2,9) are given.Find C € AB such that C-A-B and AB = 3AC

Answer 1

The point C is $(-\frac{2}{3}, -\frac{5}{3})$.

Step-by-step explanation:

Let the coordinates of C are (h,k).

Now, CAB is a straight line, where A(0,1) and B(2,9) such that AB = 3AC i.e. AB : AC = 3 : 1

Therefore, point A divides the line CB in the ratio 1 : 3 internally.

Hence, (0,1) ≡ $(\frac{3h + 1 \times 2}{3 + 1}, \frac{3k + 1 \times 9}{3 + 1})$

So, 3h + 2 = 0

⇒ h = - $\frac{2}{3}$

And, 3k + 9 = 4

⇒ 3k = - 5

⇒ k = - $\frac{5}{3}$

Hence, the point C is $(-\frac{2}{3}, -\frac{5}{3})$. (Answer)