CBSE Class 12 Math 2022 Term I Solved Paper

Question : 6 of 50

Marks: +1, -0

Three points

{\P}(2 x, x+3), {\Q}(0, x)

and

{\R}(x+3, x+6)

are collinear, then

x

is equal to

Solution:

Explanation: As points are collinear

\Rightarrow

area of triangle formed by 3 points is zero.

⇒ \;\; \;{1}/{2}{|\table (x_1-x_2) , (x_2-x_3) ; (y_1-y_2) , (y_2-y_3) |}=0

⇒ \;{1}/{2}{|\table (2 x-0) , \{0-(x+3)\} ; (x+3-x) , \{x-(x+6)\} |}=0

⇒ \;\; {|\table 2 x , -(x+3) ; 3 , -6 |}=0

⇒ \;\; -12 x+3(x+3)=0

⇒\;-12 x+3 x+9\;=0

⇒\;-9 x\;=-9

⇒\;x\;=1

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