Question

Three sides of a triangle are given by the equations $4x-7y+10=0,x+y=5$ and $7x+4y-15=0$ Then, which of the following lies on the line $2x+3y-8=0$?

• A. Centroid
• B. Incentre
• C. Orthocentre
• D. Circumcentre

Answer 1

Answer: (C)

Orthocentre

Given equation of lines are $4x-7y+10=0$ ...(i)
$x+y=5$ ...(ii)
$7x+4y-15=0$ ...(iii)
Slope of line (i) is $\frac{4}{7}$
Slope of line (ii) is $-1$
Slope of line (iii) is $-\frac{7}{4}$
$\Rightarrow$ Lines (i) and (iii) are perpendicular lines .
$\therefore △ABC$ is a right -angled triangle.
$\therefore$ 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 .