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Question
Choose the correct option for the given statements
Statement-1 : The orthocentre of the triangle, the equation of whose sides are 2x+3y-5=0, x+y=5 and 3x-2y-1=0, is (1, 1).
Statement-2: If in a triangle, orthocentre, circumcentre and centroid are lattice points, then its vertices must also be lattice points (the points whose coordinates are integers).
Statement-3: If two lines are perpendicular, then product of their slopes is -1
Choose the correct option for the given statements
Statement-1 : The orthocentre of the triangle, the equation of whose sides are 2x+3y-5=0, x+y=5 and 3x-2y-1=0, is (1, 1).
Statement-2: If in a triangle, orthocentre, circumcentre and centroid are lattice points, then its vertices must also be lattice points (the points whose coordinates are integers).
Statement-3: If two lines are perpendicular, then product of their slopes is -1
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Solution
The correct option is B TFF
Statement-1 : As 2x+3y−5=0and3x−2y−1=0 are ⊥ to each other at (1, 1). Hence, True.
Statement-2 :(x1+x2+x33,y1+y2+y33) can be rational even if x1,x2,x3 all are not rational. Hence, False.
Statement-3 : False, as it is not true for coordinate axes.
Statement-1 : As 2x+3y−5=0and3x−2y−1=0 are ⊥ to each other at (1, 1). Hence, True.
Statement-2 :(x1+x2+x33,y1+y2+y33) can be rational even if x1,x2,x3 all are not rational. Hence, False.
Statement-3 : False, as it is not true for coordinate axes.
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