Two vertices of a triangle are `(4,-3) & (-2, 5)`. If the orthocentre of the triangle is at `(1,2)`, find coordinates of the third vertex .

Options

A. `(-33,-26)`
B. `(33,26)`
C. `(26,33)`
D. none of these

Answer

B

Explanation

Let the third vertex be (h,k)

Now, the slope of AD is `(k-2)(h-1)`, the slope of BC is `(5+3)//(-2-4)=4//3`, the slope of the BE is `(-3-2)//(4-1) =-5//3`, and the slope of AC is `(k-5)(h+2)`. Since `AD bot BC` , we have
`(k-2)/(h-1)xx(-4)/(3)=1`
or `3h-4k+5=0` (1)
Again, since `BE bot AC`, we have
`(5)/(3)xx(k-5)/(h+2)=-1`
or `3h-5k+31=0`
On solving (1) and (2) , we get `h=33,h=26`, hence, the third vertex is `(33,26)`.