Question 33
Please find the ratio in which a line 3x + 4y = 2 divides the line segment joining A(-2, - 3) and B(4, 6)
Solution
The ratio $$k : 1$$ in which a line $$ax + py + c = 0$$ divides the segment joining $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:
$$\text{Ratio} = -\frac{ax_1 + by_1 + c}{ax_2 + by_2 + c}$$
Substituting the values:
Ratio = $$-\left(\frac{3\left(-2\right)+4\left(-3\right)-2}{3\left(4\right)+4\left(6\right)-2}\right)=-\left(\frac{-20}{34}\right)=\frac{10}{17}$$.
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