Math, asked by ItzMeRenu, 1 month ago

Verify whether the points (-2,3),(4,2) and (10,1) are collinear or not.

Give answer with explanation. ✌​

Answers

Answered by amitkumar44481
74

Solution :

Let,

  • x1 = - 2.
  • x2 = 4.
  • x3 = 10.
  • y1 = 3.
  • y2 = 2.
  • y3 = 1.
  • P = ( - 2 , 3 )
  • Q = ( 4 , 2 )
  • R = ( 10 , 1 )

Now, Condition for Collinear, If area of triangle become 0.

\rightarrow\tt \:A=\frac{1}{2}\left[\begin{array}{c c c} \tt - 2 &  \tt 3 &  \tt 1 \\ \tt4 &  \tt 2 &  \tt 1 \\ \tt 10 &  \tt1 &  \tt1 \end{array}\right] = 0.\\  \\

\rightarrow\tt \:A=\frac{1}{2} \bigg | - 2  \:\left[\begin{array}{c c } \tt  2 &  \tt 1 \\ \tt 1  & \tt 1 \\ \end{array}\right] - 3 \: \left[\begin{array}{c c } \tt 4 & \tt 1 \\ \tt 10 & \tt 1 \end{array}\right] + 1 \: \left[\begin{array}{c c} \tt 4 & \tt 2   \\ \tt 10 & \tt 1 \\ \end{array}\right] \bigg|  \\  \\

 \rightarrow \tt \:  A=\dfrac{1}{2} \bigg | - 2(1)(2) + 2 - 3(4)(1) + 3(10)(1) + 1(4)(1) - 1(10)(2)\bigg |  \\  \\

 \rightarrow \tt \:  A=\dfrac{1}{2} \bigg |  - 4 + 2 - 12 + 30 + 4 - 20 \bigg |   \\  \\

\rightarrow \tt \:  A=\dfrac{1}{2} \bigg |   - 36 + 36\bigg |   \\  \\

 \rightarrow\tt \:  A= 0.

Hence verify, whether the points P , Q and R are collinear.

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