(i) Find equation of line joining $(1,2)$ and $(3,6)$ using determinants. (ii) Find equation of line joining $(3,1)$ and $(9,3)$ using determinants.

Home » (i) Find equation of line joining and using determinants. (ii) Find equation of line joining and using determinants.

(i) Find equation of line joining $(1,2)$ and $(3,6)$ using determinants. (ii) Find equation of line joining $(3,1)$ and $(9,3)$ using determinants.

Let $A(x, y)$ be any vertex of a triangle.

All points are on one line if area of triangle is zero.

$\frac{1}{2}[x(2-6)-y(1-3)+1(6-6)]=0$

$-4 x+2 y=0$

$y=2 x$

Which is equation of line.

(ii) Let $A(x, y)$ be any vertex of a triangle.

All points are on one line if area of triangle is zero.

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

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

$-2 x+6 y=0$

$x-3 y=0$

Which is equation of line.

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