x + 8y – 22 = 0, 5x + 2y – 34 = 0, 2x – 3y + 13 = 0 are the three sides of a triangle. The area of the triangle is

Question

x + 8y – 22 = 0, 5x + 2y – 34 = 0, 2x – 3y + 13 = 0 are the three sides of a triangle. The area of the triangle is (A) 36 square unit (B) 19 square unit (C) 42 square unit (D) 72 square unit

Answer 1

Ans : (B)
\(:\) If AB denotes \(\quad: \quad x+8 y-22=0 \longrightarrow(1)\)
\(B C\) denotes
and CA denotes \(\quad: \quad 5 x+2 y-34=0 \longrightarrow(2)\)
Then solving equations \((1),(2)\) and \((3)\), we get
\(A \equiv(-2,3), B \equiv(6,2)\) and \(C \equiv(4,7) .\)
Hence, area of \(\triangle A B c\) is 19 square units

Answer 2

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Answer 3

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