Two of the vertices of $ riangle PQR$ are $P(-1, 5)$ and $Q(5, 2)$. The coordinates of a point which divides…

Question

Two of the vertices of $	riangle PQR$ are $P(-1, 5)$ and $Q(5, 2)$. The coordinates of a point which divides PQ in the ratio $2:1$ are:

Accepted Answer

## Model Answer **(C) (3, 3)** Using the section formula with P(−1, 5), Q(5, 2), ratio 2:1: $x = \frac{2(5)+1(-1)}{3} = 3$, $y = \frac{2(2)+1(5)}{3} = 3$. Source: Chapter 7, Section 7.3 (Section Formula) ## Explanation Apply the section formula directly: $\left(\frac{m_1x_2+m_2x_1}{m_1+m_2},\ \frac{m_1y_2+m_2y_1}{m_1+m_2}\right)$ with $m_1=2,\ m_2=1$. A common mistake is swapping the ratio or the points — always assign $m_1$ to the part nearer to the first point listed.

Mathematics — Standard (041) — CBSE Class 10 board question