The incentre of the triangle formed by the st | vedclass

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

Question

(A) The vertices of the triangle are the intersection points of the lines:$1$. $y=\sqrt{3}x$ and $y=-\sqrt{3}x$ intersect at $A(0, 0)$.$2$. $y=\sqrt{3

Vedclass · Accepted Answer

$(0, 2)$

Vedclass · Answer

(A) The vertices of the triangle are the intersection points of the lines:$1$. $y=\sqrt{3}x$ and $y=-\sqrt{3}x$ intersect at $A(0, 0)$.$2$. $y=\sqrt{3}x$ and $y=3$ intersect at $B(\sqrt{3}, 3)$.$3$. $y=-\sqrt{3}x$ and $y=3$ intersect at $C(-\sqrt{3}, 3)$.The lengths of the sides are:$c = AB = \sqrt{(\sqrt{3}-0)^2 + (3-0)^2} = \sqrt{3+9} = \sqrt{12} = 2\sqrt{3}$.$b = AC = \sqrt{(-\sqrt{3}-0)^2 + (3-0)^2} = \sqrt{3+9} = 2\sqrt{3}$.$a = BC = \sqrt{(\sqrt{3}-(-\sqrt{3}))^2 + (3-3)^2} = \sqrt{(2\sqrt{3})^2} = 2\sqrt{3}$.Since $a=b=c$,the triangle is equilateral.The incentre $(I)$ of an equilateral triangle is the same as its centroid $(G)$.$I = G = \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right) = \left(\frac{0+\sqrt{3}-\sqrt{3}}{3}, \frac{0+3+3}{3}\right) = \left(0, \frac{6}{3}\right) = (0, 2)$.

The incentre of the triangle formed by the straight lines $y=\sqrt{3}x$,$y=-\sqrt{3}x$ and $y=3$ is

Similar Questions

If the vertices of a triangle are $(a, b - c)$,$(b, c - a)$,and $(c, a - b)$,then the centroid of the triangle lies

In $\Delta ABC$,the coordinates of $B$ are $(0, 0)$,$AB = 2$,$\angle ABC = \frac{\pi}{3}$,and the coordinates of the midpoint of $BC$ are $(2, 0)$. Find the centroid of the triangle.

The orthocenter of the triangle formed by the lines $4x - 7y + 10 = 0$,$x + y - 5 = 0$,and $7x + 4y - 15 = 0$ is:

Two vertices of a triangle are $(5, -1)$ and $(-2, 3)$. If the origin $(0, 0)$ is the orthocentre of this triangle,then the coordinates of the third vertex of that triangle are

If the line $bx + ay = 3ab$ intersects the coordinate axes at points $A$ and $B$,then the centroid of $\Delta OAB$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module