- AQ
- BR
- CP
- DS
Step-by-Step Solution
A , B : slope of AB . For P , slope of BP , the same, so A, B, P are collinear (area of triangle ABP ). Q, R and S give other slopes.
Answer: C) P
Points A and B are joined, and four more points P, Q, R and S are plotted. Which of P, Q, R, S is collinear with A and B?
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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