Straight Lines
Straight Lines
nta_pyq_2025_jan
Grade 11
Question:
Let the area of a △P QR with vertices P (5, 4), Q(-2, 4) and R(a, b) be 35 square units. If its orthocenter and centroid are O (2, 14 5 ) and C(c, d) respectively, then c + 2d is equal to
Step-by-Step Solution
Key Concept: Apply the core result for lines, slopes and distances and simplify using the given constraints.
(4) Equation of lines QR = 5x + 2y + 2 = 0 Equation of lines P R = 10x - 3y - 38 = 0 \therefore Point R(2, -6) 5 - 2 + 2 4 + 4 - 6 Centroid = ( , ) 3 3 5 2 = ( , ) 3 3 5 4 c + 2d = + = 3 3 3
Correct Answer: 4