Let the area of a △ PQR with vertices P ( 5 , 4 ) , Q ( − 2 , 4 ) and R ( a , b ) be 35 square units. If its orthocenter and centroid are O ( 2 , 5 14 ) and C ( c , d ) respectively, then c + 2 d is

Question

Let the area of a △ PQR with vertices P ( 5 , 4 ) , Q ( − 2 , 4 ) and R ( a , b ) be 35 square units. If its orthocenter and centroid are O ( 2 , 5 14 ​ ) and C ( c , d ) respectively, then c + 2 d is equal to

TestHub · Accepted Answer

​ Equation of lines QR = 5 x + 2 y + 2 = 0 Equation of lines PR = 10 x − 3 y − 38 = 0 ∴ Point R ( 2 , − 6 ) Centroid = ( 3 5 − 2 + 2 ​ , 3 4 + 4 − 6 ​ ) = ( 3 5 ​ , 3 2 ​ ) c + 2 d = 3 5 ​ + 3 4 ​ = 3 ​

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