If the mid-points of the sides $B C, C A$ and $A B$ of a triangle $A B C$, are respectively $(2,1)$, $(-1,-2)$ and $(3,3)$, then the equation of the side $B C$ is

Question

If the mid-points of the sides $B C, C A$ and $A B$ of a triangle $A B C$, are respectively $(2,1)$, $(-1,-2)$ and $(3,3)$, then the equation of the side $B C$ is, $x-2 y=0$, $5 x-4 y=6$, $2 x+3 y=8$, $3 x-2 y=6$

MARKS App · Accepted Answer

Let the coordinate of $B$ is $(a, b)$. Mid-point of $B Q=$ Mid-point of $P R$ $\begin{aligned} & \Rightarrow \quad\left(\frac{a-1}{2}, \frac{b-2}{2}\right)=\left(\frac{3+2}{2}, \frac{3+1}{2}\right) \ & \Rightarrow \quad \frac{a-1}{2}=\frac{5}{2} \ & \text{and } \frac{b-2}{2}=\frac{4}{2} \ & \Rightarrow \quad a=5+1 \ & \text{and } b=4+2 \ & \Rightarrow \quad a=6 \text { and } b=6 \end{aligned}$ $\therefore \quad B(6,6)$ and $P(2,1)$ Now, equation of $B C$ is $\begin{array}{rlrl} & y-6=\frac{1-6}{2-6}(x-6) \ \Rightarrow & y-6=\frac{-5}{-4}(x-6) \ \Rightarrow & 4 y-24=5 x-30 \ \Rightarrow & 5 x-4 y-30+24=0 \ \Rightarrow & 5 x-4 y=6 \end{array}$

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