The base of an equilateral triangle with side | vedclass

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

Question

(N/A) Let $ABC$ be the equilateral triangle with side $2a$.Since the base $BC$ lies along the $y$-axis with its mid-point at the origin $O(0,0)$,the c

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) Let $ABC$ be the equilateral triangle with side $2a$.
Since the base $BC$ lies along the $y$-axis with its mid-point at the origin $O(0,0)$,the coordinates of $B$ and $C$ are $(0, a)$ and $(0, -a)$ (or vice versa).
The altitude from vertex $A$ to the base $BC$ lies along the $x$-axis because the altitude of an equilateral triangle is perpendicular to the base.
In $\Delta AOC$,where $O$ is the origin,$AC = 2a$ and $OC = a$.
Using the Pythagorean theorem: $(AC)^2 = (OA)^2 + (OC)^2$
$(2a)^2 = (OA)^2 + a^2$
$4a^2 = (OA)^2 + a^2$
$(OA)^2 = 3a^2$
$OA = \sqrt{3}a$
Since $A$ lies on the $x$-axis,its coordinates are $(\sqrt{3}a, 0)$ or $(-\sqrt{3}a, 0)$.
Thus,the vertices of the triangle are $(0, a), (0, -a), (\sqrt{3}a, 0)$ or $(0, a), (0, -a), (-\sqrt{3}a, 0)$.

The base of an equilateral triangle with side $2a$ lies along the $y$-axis such that the mid-point of the base is at the origin. Find the vertices of the triangle.

Similar Questions

In $\triangle ABC$,if $A=(1,2)$ and the equations of the medians through $B$ and $C$ are $x+y=5$ and $x=4$ respectively,then the area of $\triangle ABC$ is

Let $O(0,0), P(3,4), Q(6,0)$ be the vertices of the triangle $OPQ$. The point $R$ inside the triangle $OPQ$ is such that the triangles $OPR, PQR, OQR$ are of equal area. The coordinates of $R$ are

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

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:

Two vertices of a triangle are $(5, -1)$ and $(-2, 3)$. If the orthocentre is the origin,then the coordinates of the third vertex are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module