Three lines 2 x + 3 y − 1 = 0 , x + 2 y − 1 = 0 , and a x + b y − 1 = 0 form a triangle with orthocentre at the origin. Find ( b − a ) /4 .

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TestHub · Accepted Answer

The first two lines intersect at (-1, 1). Since the origin lies on its altitude, the third side must have slope 1, giving b = − a . Orthogonality of another altitude determines a = − 8 , b = 8 ; thus ( b − a ) /4 = 4 .

Mathematics - Properties of Triangle Question with Solution | TestHub

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