Q69.Let S be the set of all triangles in the xy -plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is: (1) 36 (2) 32 (3) 9 (4) 18
What This Question Tests
This question involves calculating the area of a triangle with vertices on coordinate axes and at the origin, then finding the number of integer coordinate pairs that satisfy a given area condition.
Concepts Tested
Formulas Used
Area = (1/2) |x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)|
Area = (1/2) |ab| for vertices (0,0), (a,0), (0,b)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Area of triangle, Integral coordinates
- Year
- 2019
- Shift
- 09 Jan Shift 2
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 10 Mathematics Ch 7: Coordinate Geometry, Class 11 Mathematics Ch 10: Straight Lines
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