What is the orthocenter of the triangle with | vedclass

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

Question

(B) Let the vertices be $A(2, \frac{\sqrt{3}-1}{2})$,$B(\frac{1}{2}, -\frac{1}{2})$,and $C(2, -\frac{1}{2})$.Calculate the lengths of the sides:$AB^2

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Let the vertices be $A(2, \frac{\sqrt{3}-1}{2})$,$B(\frac{1}{2}, -\frac{1}{2})$,and $C(2, -\frac{1}{2})$.Calculate the lengths of the sides:$AB^2 = (2 - \frac{1}{2})^2 + (\frac{\sqrt{3}-1}{2} - (-\frac{1}{2}))^2 = (\frac{3}{2})^2 + (\frac{\sqrt{3}}{2})^2 = \frac{9}{4} + \frac{3}{4} = 3$.$BC^2 = (2 - \frac{1}{2})^2 + (-\frac{1}{2} - (-\frac{1}{2}))^2 = (\frac{3}{2})^2 + 0 = \frac{9}{4}$.$CA^2 = (2 - 2)^2 + (\frac{\sqrt{3}-1}{2} - (-\frac{1}{2}))^2 = 0 + (\frac{\sqrt{3}}{2})^2 = \frac{3}{4}$.Since $BC^2 + CA^2 = \frac{9}{4} + \frac{3}{4} = \frac{12}{4} = 3 = AB^2$,the triangle is a right-angled triangle with the right angle at vertex $C(2, -\frac{1}{2})$.In a right-angled triangle,the orthocenter is the vertex where the right angle is located.Therefore,the orthocenter is $C(2, -\frac{1}{2})$.

What is the orthocenter of the triangle with vertices $(2, \frac{\sqrt{3}-1}{2})$,$(\frac{1}{2}, -\frac{1}{2})$,and $(2, -\frac{1}{2})$?

Similar Questions

If $P$ is a point equidistant from all the vertices $A(-1, 3)$,$B(3, 5)$,and $C(5, 7)$ of a triangle $ABC$,then $PA=$

The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points $(a^2 + 1, a^2 + 1)$ and $(2a, -2a)$,where $a \ne 0$. Then for any $a$,the orthocentre of this triangle lies on the line:

If the vertices of a triangle are $(-2,3), (6,-1)$ and $(4,3)$,then the coordinates of the circumcentre of the triangle are

The orthocenter of the triangle whose sides are given by $x+y+10=0$,$x-y-2=0$,and $2x+y-7=0$ is

If the orthocentre of the triangle,whose vertices are $(1,2), (2,3)$ and $(3,1)$ is $(\alpha, \beta)$,then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module