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Question

# Three sides of a triangle are given by the equations 4xâˆ’7y+10=0,x+y=5 and 7x+4yâˆ’15=0 Then, which of the following lies on the line 2x+3yâˆ’8=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 OrthocentreGiven equation of lines are 4x−7y+10=0 ...(i)x+y=5 ...(ii)7x+4y−15=0 ...(iii)Slope of line (i) is 47Slope of line (ii) is −1Slope 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+3y−8=0.Clearly, B cannot be the centroid,incentre or the circumcentre .

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