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Question

# The equation of the sides of a triangle are xâˆ’3y=0,4x+3y=5 and 3x+y=0. The line 3xâˆ’4y=0 passes through:

A
the incentre
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B
the centroid
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C
the orthocentre
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D
the circumcentre
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Solution

## The correct option is D the orthocentreGiven equation of line are,l1:x−3y=0 ,Slope m1=13l2:4x+3y=5 slope m2=−43l3:3x+y=0 slope m3=−3Here m1×m3=−1 Line l1⊥l3Slope of given line:3x−4y=0,m=34herem×m2=−1∴ Given line is perpendicular to Linel2Therefore The given line must pass throigh the orthocenter

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