Please answer the question in detail and fast. Q.Consider a triangle ABC whose sides AB,BC,AC are represented by the straight lines 2x+3y=0, x+py=q, x-y=3 respectively The point P is (2,3) then solve Q.13

Please answer the question in detail and fast. Q.Consider a triangle ABC whose sides AB,BC,AC are represented by the straight lines 2x+3y=0, x+py=q, x-y=3 respectively The point P is (2,3) then solve Q.13 13. 14. 15. If P is the centroid, then (p + q) equals (A) 47 (C) 65 If P is the orthocenter, then (p + q) equals (A) 47 (C) 65 If P is the circumcenter, then (p + q) equals (A) 47 (C) 65 (B) 50 (D) 74 (B) 50 (D) 74 (B) 50 (D) 74

Hi, 
The equation  2x+3y=0 will be 2x+y = 0 only then option will match. So correcting the same and providing solution 
2 straight x plus straight y space equals space 0 space.... open parentheses 1 close parentheses straight x plus py space equals space straight q... open parentheses 2 close parentheses straight x minus straight y space equals space 3.... open parentheses 3 close parentheses add space first space and space last space 3 straight x space equals space 3 space straight x space equals space 1 space so space straight y space equals space minus 2 space So space straight A thin space equals space open parentheses 1 comma negative 2 close parentheses now space AC space is space straight x minus straight y space equals space 3 space so space let space straight x space equals space straight beta space so space straight y space equals space straight beta minus 3 and space AB thin space is space 2 straight x plus straight y space equals space 0 space so space let space straight x space equals space straight alpha space so space straight y space equals space minus 2 straight alpha




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