Find equation of line joining (3,1) and (9,3) using determinants

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3 and 4 .Determinants and Matrices

easy

Find equation of line joining $(3,1)$ and $(9,3)$ using determinants

A

$x-3 y=2$

B

$x-3 y=0$

C

$x+3 y=0$

D

$x-3 y=10$

Solution

Let $P(x, y)$ be any point on the line joining points $A(3,1)$ and $B(9,3) .$

Then, the points $A, B$ and $P$ are collinear. Therefore, the area of the triangle $ABP$ will be zero.

$\therefore \frac{1}{2}\left|\begin{array}{lll}3 & 1 & 1 \\ 9 & 3 & 1 \\ x & y & 1\end{array}\right|=0$

$\Rightarrow \frac{1}{2}[3(3-y)-1(9-x)+1(9 y-3 x)]=0$

$\Rightarrow 9-3 y-9+x+9 y-3 x=0$

$\Rightarrow 6 y-2 x=0$

$\Rightarrow x-3 y=0$

Hence, the equation of the line joining the given points is $x-3 y=0$

Standard 12

Mathematics

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