Question

Find the point which is two third of the way from P(0,1)to Q(1,0).​

Answer 1

Points:

• $P(x_{1}, y_{1}) = (0,1)$
• $Q(x_{2}, y_{2}) = (1,0)$

Ratio is m : n or 2 : 3

By Section Formula we have,

$(x_{3},y_{3}) = \left(\frac{mx_{2} + nx_{1}}{m + n}\; , \; \frac{my_{2} + ny_{1}}{m+n} \right) \\ \Rightarrow \qquad \left( \frac{2 \cdot 1 + 3 \cdot 0}{2+3} \; , \; \frac{2 \cdot 0 + 3 \cdot 1}{2+3} \right)</p><p>\\ \Rightarrow \qquad \left( \frac{2 + 0}{5} \; , \; \frac{0 + 3}{5} \right) \\ \Rightarrow \qquad \left( \frac{2}{5} \; , \; \frac{3}{5} \right)$

ANSWER: $\left( \frac{2}{5} \; , \; \frac{3}{5} \right)$