Question

In the given figure, the line segment AB meets x-axis at A and y-axis at B. The point \(\mathrm{P}(-3, 1)\) on AB divides it in the ratio 2 : 3. Find the co-ordinates of A and B.
[Hint: (i) The co-ordinates of A and B are of the form A(x, 0), and B(0, y).]

Answer 1

Let $$A(x, 0)$$ and $$B(0, y)$$.

Since $$P(-3, 1)$$ divides AB in the ratio $$2 : 3$$, the co-ordinates of P are $$\left(\frac{2 \times 0 + 3 \times x}{2 + 3}, \frac{2 \times y + 3 \times 0}{2 + 3}\right)$$

Comparing with $$P(-3, 1)$$:

$$\frac{3x}{5} = -3$$

$$\Rightarrow x = -5$$

$$\frac{2y}{5} = 1$$

$$\Rightarrow y = \frac{5}{2}$$

Hence the co-ordinates of A are $$A(-5, 0)$$ and of B are $$B\left(0, \frac{5}{2}\right)$$.