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3 and 4 .Determinants and Matrices
easy
નિશ્ચાયકનો ઉપયોગ કરી $(1, 2)$ અને $(3, 6)$ ને જોડતી રેખાનું સમીકરણ શોધો.
A
$y=2 x$
B
$y=3 x$
C
$y=4 x+7$
D
$y=2 x+9$
Solution
Let $P(x, y)$ be any point on the line joining points $A(1,2)$ and $B(3,6) .$ Then, the points $A,=$ and $P$ are collinear. Therefore, the area of triangle $ABP$ will be zero.
$\therefore \frac{1}{2}\left|\begin{array}{lll}1 & 2 & 1 \\ 3 & 6 & 1 \\ x & y & 1\end{array}\right|=0$
$\Rightarrow \frac{1}{2}[1(6-y)-2(3-x)+1(3 y-6 x)]=0$
$\Rightarrow 6-y-6+2 x+3 y-6 x=0$
$\Rightarrow 2 y-4 x=0$
$\Rightarrow y=2 x$
Hence, the equation of the line joining the given points is $y=2 x$
Standard 12
Mathematics
