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Question

Three sides of a triangle are given by the equations 4x7y+10=0,x+y=5 and 7x+4y15=0 Then, which of the following lies on the line 2x+3y8=0?

A
Centroid
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B
Incentre
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C
Orthocentre
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D
Circumcentre
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Solution

The correct option is B Orthocentre
Given equation of lines are 4x7y+10=0 ...(i)
x+y=5 ...(ii)
7x+4y15=0 ...(iii)
Slope of line (i) is 47
Slope of line (ii) is 1
Slope of line (iii) is 74
Lines (i) and (iii) are perpendicular lines .
ABC is a right -angled triangle.
Point B, the intersection of these lines, is the orthocentre.
Coordinates of B are (1,2).
Also, B(1,2) satisfies the equation 2x+3y8=0.
Clearly, B cannot be the centroid,incentre or the circumcentre .
126961_44306_ans_06098109588e4a90a2b654060f254d48.png

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