- A29
- B32
- C64
- D35
Step-by-Step Solution
Area = (64) = 32 sq units.
Answer: B) 32
Find the area of the triangle with vertices (−5, −1), (3, −5), (5, 2).
Class 10Coordinate GeometryGeometry — Coordinates
Key idea: Area of a triangle from vertices
Given A₁, ₁), B₂, ₂), C₃, ₃), the area is:
**Area = ₁₂ − ₃) + ₂₃ − ₁) + ₃₁ − ₂)|**
The absolute value sign |·| ensures area is positive regardless of vertex order.
**Use case 1**: Compute area without drawing anything.
**Use case 2**: Test for COLLINEARITY — three points are collinear iff the (signed) area expression equals 0.
**Example**: A(1, 1), B(2, 3), C(4, 5).
Area = ·2 = 1.
Non-zero → not collinear.
**Area = ₁₂ − ₃) + ₂₃ − ₁) + ₃₁ − ₂)|**
The absolute value sign |·| ensures area is positive regardless of vertex order.
**Use case 1**: Compute area without drawing anything.
**Use case 2**: Test for COLLINEARITY — three points are collinear iff the (signed) area expression equals 0.
**Example**: A(1, 1), B(2, 3), C(4, 5).
Area = ·2 = 1.
Non-zero → not collinear.
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