Question

A triangle ABC with vertices $A(-1,0),B(-2,\frac{3}{4}),\&C(-3,\frac{-7}{6})$ has its orthocentre H. Then the orthocentre of triangle BCH will be

• A. $(-3,-2)$
• B. $(1,3)$
• C. $(-1,2)$
• D. none of these

Answer 1

Answer: (D)

none of these

The ortho-center is the point where all three altitudes of the triangle intersect.

Given, $H$ is the ortho-centre of $△ABC$

It is obvious that the ortho-centre of $△BHC$ is $A$

Consider $△BHC$,

$HF,BK,CL$ are the altitudes

On extending these altitude to meet at a point, which is the ortho-centre, we can see that they meet at $A$.

Hence, $A(-1,0)$ is the ortho-centre of $△BHC$. It is not in the given options.