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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
Find equation of line joining $(1,2)$ and $(3,6)$ using determinates
  • ✓
    $y=2 x$
  • B
    $y=3 x$
  • C
    $y=4 x+7$
  • D
    $y=2 x+9$
✓

Answer

Correct option: A.
$y=2 x$
a
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 $y=2 x$

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