Question
What is the area of triangle ABC with vertices A(1, 2),
B(5, 6), and C(7, 2)?Solution
ATQ, Use the coordinate area formula: Area = (1/2) · |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. Let A(1,2) → (x₁,y₁), B(5,6) → (x₂,y₂), C(7,2) → (x₃,y₃). Compute: y₂ − y₃ = 6 − 2 = 4 y₃ − y₁ = 2 − 2 = 0 y₁ − y₂ = 2 − 6 = −4 x₁(y₂ − y₃) = 1 × 4 = 4 x₂(y₃ − y₁) = 5 × 0 = 0 x₃(y₁ − y₂) = 7 × (−4) = −28 Sum = 4 + 0 − 28 = −24 Area = (1/2) · |−24| = 12 square units.
1500 150 30 ? 3.6 1.8
32, 52, 82, 124, 180, ?
625, 125, 375, 75, 225, 45, ?
What value should come in the place of (?) in the following number series?
71, 72, 76, 103, ?, 244257, 399, 566, ?, 983, 1237
31 32 35 ? 47 56
...What will come in place of the question mark (?) in the following series?
206, 187, ?, 157, 146, 139
- Find the missing number in the given number series.
42, 37, 45, 40, 48, ? 13, 29, 65, 129, ?, 373
What will come in place of the question mark (?) in the following series?
130, 158, 214, 298, ?, 550
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