The orthocentre of the triangle with vertices | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the vertices be $A = \left( 2, \frac{\sqrt{3} - 1}{2} \right)$,$B = \left( \frac{1}{2}, -\frac{1}{2} \right)$,and $C = \left( 2, -\frac{1}{2}

Vedclass · Accepted Answer

$\left( 2, -\frac{1}{2} \right)$

Vedclass · Answer

(B) Let the vertices be $A = \left( 2, \frac{\sqrt{3} - 1}{2} \right)$,$B = \left( \frac{1}{2}, -\frac{1}{2} \right)$,and $C = \left( 2, -\frac{1}{2} \right)$.Observe that the side $AC$ is vertical (both $x$-coordinates are $2$) and the side $BC$ is horizontal (both $y$-coordinates are $-\frac{1}{2}$).Since $AC$ is perpendicular to $BC$,the triangle is a right-angled triangle with the right angle at vertex $C = \left( 2, -\frac{1}{2} \right)$.In a right-angled triangle,the orthocentre is the vertex where the right angle is located.Therefore,the orthocentre is $\left( 2, -\frac{1}{2} \right)$.

The orthocentre of the triangle with vertices $\left( 2, \frac{\sqrt{3} - 1}{2} \right)$,$\left( \frac{1}{2}, -\frac{1}{2} \right)$,and $\left( 2, -\frac{1}{2} \right)$ is:

Similar Questions

If the vertices of a triangle are $(a, 1), (b, 3),$ and $(4, c),$ then the centroid of the triangle will lie on the $x$-axis if

The two vertices of a triangle are $(-1, 4)$ and $(5, 2)$. If its centroid is $(0, -3)$,find the third vertex.

What is the distance of the orthocenter from the vertex of a triangle with vertices $(2, 3), (4, 5),$ and $(-1, 10)$?

The quadratic equation whose roots are the coordinates of the circumcentre of the triangle formed by the points $(-2,-1), (6,-1),$ and $(2,5)$ is

The orthocentre of the triangle formed by the lines $x + y = 1$,$2x + 3y = 6$,and $4x - y + 4 = 0$ lies in which quadrant?

Vedclass Test Series

Exam Paper Generator

Online Exam Module