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प्रश्न
Answer the following question:
Find the value of k:
If area of triangle is `33/2` square unit and vertices are L(3, −5), M(−2, k), N(1, 4)
उत्तर
Here, L(x1, y1) ≡ L(3,− 5), M(x2, y2) ≡ M(−2, k), N(x3, y3) ≡ N(1, 4)
A(ΔLMN) = `33/2"sq. units"`
Area of a triangle = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`
∴ `± 33/2 = 1/2|(3, -5, 1),(-2, "k", 1),(1, 4, 1)|`
∴ `± 33/2 = 1/2[3("k" - 4) - (-5)(-2 - 1) + 1(-8 - "k")]`
∴ ± 33 = 3k – 12 – 15 – 8 – k
∴ ± 33 = 2k – 35
∴ 2k – 35 = 33 or 2k – 35 = –33
∴ 2k = 68 or 2k = 2
∴ k = 34 or k = 1
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