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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 6 of 50
Marks: +1, -0
Three points P(2x,x+3),Q(0,x)P(2 x, x+3), Q(0, x) and R(x+3,x+6)R(x+3, x+6) are collinear, then xx is equal to
Solution:     👈: Video Solution
Explanation: As points are collinear
⇒\Rightarrow area of triangle formed by 3 points is zero.
⇒12∣(x1−x2)(x2−x3)(y1−y2)(y2−y3)∣=0\Rightarrow \frac{1}{2}\begin{vmatrix} (x_1-x_2) & (x_2-x_3) \\ (y_1-y_2) & (y_2-y_3) \end{vmatrix}=0
⇒12∣(2x−0){0−(x+3)}(x+3−x){x−(x+6)}∣=0\Rightarrow \frac{1}{2}\begin{vmatrix} (2x-0) & \{0-(x+3)\} \\ (x+3-x) & \{x-(x+6)\} \end{vmatrix}=0
⇒∣2x−(x+3)3−6∣=0\Rightarrow \begin{vmatrix} 2x & -(x+3) \\ 3 & -6 \end{vmatrix}=0
⇒−12x+3(x+3)=0\Rightarrow -12x+3(x+3)=0
⇒−12x+3x+9=0\Rightarrow -12x+3x+9=0
⇒−9x=−9\Rightarrow -9x=-9
⇒x=1\Rightarrow x=1
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