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Co-Ordinate Geometry — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsCo-Ordinate Geometry3 Marks
Question
The line segment joining the points $A(3, -4)$ and $B(1, 2)$ is trisected at the points $P(p, -2)$ and $\text{Q}\Big(\frac{5}{3},\text{q}\Big).$ Find the values of $p$ and $q.$
✓

Answer

Point $P$ divides the join of $A(3, -4)$ and $B(1, 2)$ in the ratio $1 : 2$
Coordinates of $P$ are:
$\Big(\frac{1\times1+2\times3}{1+2},\frac{1\times2+2\times(-4)}{1+2}\Big)$ or $\Big(\frac{7}{3},\frac{-6}{3}\Big)$ or $(\frac{7}{3}, -2)$
Also the point $P$ is $(p, -2) ⇒ \text{P}=\frac{7}{3}$
Further $Q$ is the midpoint of $PB$ when
$\text{P}\Big(\frac{7}{3},-2\Big)$ and $B(1, 2)$
$\therefore$ coordinates of $Q$ are $\bigg(\frac{\frac{7}{3}+1}{2},\frac{-2+2}{2}\bigg)$ or $\Big(\frac{5}{3},0\Big)$
Also, $Q$ is $\Big(\frac{5}{3},\text{q}\Big)\Rightarrow\text{q}=0$
Hence, $\text{p}=\frac{7}{3}$ and $q = 0$

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