Straight Line and Pair of Straight Lines 3 Question 10
11.
If $\left|\begin{array}{lll}x _1 & y _1 & 1 \\ x _2 & y _2 & 1 \\ x _3 & y _3 & 1\end{array}\right|=\left|\begin{array}{lll}a _1 & b _1 & 1 \\ a _2 & b _2 & 1 \\ a _3 & b _3 & 1\end{array}\right|$, then the two triangles with vertices $\left(x _1, y _1\right),\left(x _2, y _2\right),\left(x _3, y _3\right)$ and $\left(a _1, b _1\right),\left(a _2, b _2\right)$, $\left(a _3, b _3\right)$ must be congruent.
(1985, 1M)
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Answer:
Correct Answer: 11. False
Solution:
- Since, $\left|\begin{array}{lll}x _1 & y _1 & 1 \\ x _2 & y _2 & 1 \\ x _3 & y _3 & 1\end{array}\right|=\left|\begin{array}{lll}a _1 & b _1 & 1 \\ a _2 & b _2 & 1 \\ a _3 & b _3 & 1\end{array}\right|$
represents area of triangles are equal, which does not impies triangles are congrvent. Hence, given statement is false.
