- ANo, area is not zero
- BYes, area is zero
- CCannot be determined
- DYes, all are equidistant
Step-by-Step Solution
Area = (22) = 11 ≠ 0. Not collinear.
Answer: A) No, area is not zero
If A(1, 5), B(2, 3) and C(−2, −11) — find whether these three points are collinear.
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.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Coordinate Geometry practice questions
More Class 10 Coordinate Geometry practice
Find the point that trisects (divides into three equal parts) the segment from A(2, −2)…A triangle has area 0 from its vertex coordinates. What does this indicate?Find the area of the triangle with vertices (−5, −1), (3, −5), (5, 2).Two vertices of a triangle are (3, 2) and (−2, 1). Its centroid is (5/3, -1/3). Find the…Which of the following best describes the centroid of a triangle?