Question

Assertion :Two vertices of a triangle are $(-2,3)$ and $(-4,-7)$. If the orthocentre of the triangle is the origin, the coordinates of the third vertex are $(5,-1)$. Reason: Orthocentre of a triangle is equidistant from the sides of the triangle.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Let B and C be the given vertices and let $A(h,k)$ be the third vertex.
The slope of BC is $\frac{-7-3}{-4+2}=\frac{-10}{-2}=5$
Hence the slope of AD is $-\frac{1}{5}$.
But the slope of AD or AO is $\frac{k}{h}$.
We therefore obtain
$\frac{k}{h}=-\frac{1}{5}$ ...(1)
Again, slope of BO or BE is $-\frac{3}{2}$
and slope of CA is $\frac{k+7}{h+4}$
Hence $\frac{k+7}{h+4}\times -\frac{3}{2}=-1$ ...(2)
Solving (1) and (2) we get
$h=5$ and $k=-1$