Q5. Let the triangle PQR be the image of the triangle with vertices (1, 3), (3, 1) and (2, 4) in the line x + 2y = 2. If the centroid of △PQR is the point (α, β), then 15(α −β) is equal to : (1) 19 (2) 24 (3) 21 (4) 22
What This Question Tests
This multi-step problem requires finding the image of a centroid of a triangle after reflection in a line, which simplifies calculations compared to reflecting each vertex.
Concepts Tested
Formulas Used
Centroid: ((x1+x2+x3)/3, (y1+y2+y3)/3)
Formula for image of (x,y) in ax+by+c=0: (x'-x)/a = (y'-y)/b = -2(ax+by+c)/(a^2+b^2)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Reflection of a point/triangle in a line
- Year
- 2025
- Shift
- 22 Jan Shift 1
- Q Number
- Q5
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
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