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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
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Find the orthocentre of $\Delta ABC$ whose vertices are $A(0,1),B(-1,0),C(1,0)$.

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

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1 Answer

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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
Slope of $ AC=\large\frac{0-1}{1-0}$$=-1$
Since the altitude through $B$ is $\perp$ to $BC$,
Slope of the altitude through $B$ is $1$
Equation of the altitude through $B$ is given by
$y-0=1(x+1)$
$y-1=x$.......(ii)
Hence we have two altitude equations $x=0$ & $y-1=x$
Step 3
Orthocentre is the intersecting point of the altitudes (i) and (ii).
Solving (i) and (ii) we get $x=0$ and $y=1$
$\therefore$ The orthocentre is $(0,1)$
Hence (b) is the correct answer.
answered Feb 5, 2014 by sreemathi.v
edited Mar 17, 2014 by rvidyagovindarajan_1
 

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