Browse Questions

# Find the orthocentre of $\Delta ABC$ whose vertices are $A(0,1),B(-1,0),C(1,0)$.

$(a)\;(0,2)\qquad(b)\;(0,1)\qquad(c)\;(2,0)\qquad(d)\;(1,0)$

Toolbox:
• Orthocentre is the interesting point of altitudes.
• Slope of the line joining $(x_1,y_1)$ and $x_2,y_2)$ is $\large\frac{y_2-y_1}{x_2-x_1}$
Orthocentre is the interesting point of altitudes.
Step 1
Find the equation of the altitude which is perpendicular to BC and passes through A.
Slope of $BC=\large\frac{0}{1+1}$$=0=m_1 Since the altitude through A is \perp to BC, slope of the altitude =-\large\frac{1}{0} Hence the equation of the altitude passing through A(0,1) is (y-1)=\large\frac{-1}{0}$$(x-0)$
$i.e.,\:x=0$.........(i)
Step 2