Question

In what ratio is the segment joining the points \(\mathrm{A}(6,5)\) and \(\mathrm{B}(-3, 2)\) divided by the y-axis? Find the point at which the y-axis cuts AB.

Answer 1

Let the y-axis cut AB in the ratio $$m : 1$$ at the point $$(0, y)$$.

Since the x-coordinate is 0, 

$$\frac{m \times (-3) + 1 \times 6}{m + 1} = 0$$ 

$$\Rightarrow -3m + 6 = 0$$

$$\Rightarrow m = 2$$

Hence the y-axis divides AB in the ratio $$2 : 1$$.

The y-coordinate of the point of cut is $$y = \frac{2 \times 2 + 1 \times 5}{2 + 1}$$

$$= \frac{4 + 5}{3}$$

$$= \frac{9}{3}$$

$$= 3$$

Hence the y-axis cuts AB at $$(0, 3)$$.