SATHEE: Straight Line and Pair of Straight Lines 3 Question 10

Straight Line and Pair of Straight Lines 3 Question 10

11. If $| \begin{array}{lll} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{array} | = | \begin{array}{lll} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{array} |$ , then the two triangles with vertices $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ and $(a_{1}, b_{1}), (a_{2}, b_{2})$ , $(a_{3}, b_{3})$ must be congruent.

(1985, 1M)

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Answer:

Correct Answer: 11. False

Solution:

Since, $| \begin{array}{lll} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{array} | = | \begin{array}{lll} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{array} |$

represents area of triangles are equal, which does not impies triangles are congrvent. Hence, given statement is false.

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Straight Line and Pair of Straight Lines 3 Question 10

11. If |x1y11 x2y21 x3y31|=|a1b11 a2b21 a3b31|, then the two triangles with vertices (x1,y1),(x2,y2),(x3,y3) and (a1,b1),(a2,b2), (a3,b3) must be congruent.

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