Question

Find the point which divides the line segment joining the points (2, 5) and (1, -6) in the ratio 2 : 1.

• A. $(\frac{1}{3}$, $\frac{-5}{3})$
• B. $(\frac{4}{3}$, $\frac{-7}{3})$
• C. $(\frac{4}{3}$, $\frac{7}{3})$
• D. $(\frac{-7}{3}$, $\frac{4}{3})$

Answer 1

The correct option is B $(\frac{4}{3}$, $\frac{-7}{3})$

Given: Points (2, 5) and (1, -6), Ratio = 2: 1

Let point (x, y) divides the line segment joining the points (2, 5) and (1, -6) in the ratio 2 : 1.

So,
x = $\frac{\left(2\right)\left(1\right)+\left(1\right)\left(2\right)}{2+1}$
x = $\frac{2+2}{3}$
​​​​​​​x = $\frac{4}{3}$
​​​​​​​
Similarly,
y = $\frac{\left(2\right)(-6)+\left(1\right)\left(5\right)}{2+1}$
y = $\frac{-12+5}{3}$
y = $\frac{-7}{3}$
Hence, the point is ($\frac{4}{3}$, $\frac{-7}{3}$)