The equations y = pm sqrt{3}x and y = 1 repre | vedclass

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

Question

(A) The given equations are $y = \sqrt{3}x$, $y = -\sqrt{3}x$, and $y = 1$.These can be written as $y = 	an(60^{\circ})x$, $y = 	an(120^{\circ})x$,

Vedclass · Accepted Answer

an equilateral triangle

Vedclass · Answer

(A) The given equations are $y = \sqrt{3}x$, $y = -\sqrt{3}x$, and $y = 1$.These can be written as $y = 	an(60^{\circ})x$, $y = 	an(120^{\circ})x$, and $y = 1$.The lines $y = \sqrt{3}x$ and $y = -\sqrt{3}x$ pass through the origin $(0,0)$ and make angles of $60^{\circ}$ and $120^{\circ}$ with the positive $x$-axis, respectively.The angle between these two lines is $120^{\circ} - 60^{\circ} = 60^{\circ}$.The line $y = 1$ intersects $y = \sqrt{3}x$ at $(\frac{1}{\sqrt{3}}, 1)$ and $y = -\sqrt{3}x$ at $(-\frac{1}{\sqrt{3}}, 1)$.The length of the base on the line $y = 1$ is $\frac{1}{\sqrt{3}} - (-\frac{1}{\sqrt{3}}) = \frac{2}{\sqrt{3}}$.The lengths of the other two sides are $\sqrt{(\frac{1}{\sqrt{3}})^2 + 1^2} = \sqrt{\frac{1}{3} + 1} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$.Since all three sides are equal to $\frac{2}{\sqrt{3}}$, the triangle is an equilateral triangle.

The equations $y = \pm \sqrt{3}x$ and $y = 1$ represent the sides of which triangle?

Similar Questions

If the points $(1, 1)$,$(-1, -1)$,and $(-\sqrt{3}, \sqrt{3})$ are the vertices of a triangle,then this triangle is:

The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c$,where $c$ is a constant. The coordinates of the other two vertices are:

Find the area of the triangle formed by the two rays of the equation $y = |x|$ and the line $x + 2y = 2$.

The perimeter of a triangle is $16 \text{ cm}$, one of the sides is of length $6 \text{ cm}$. If the area of the triangle is $12 \text{ cm}^2$, then the triangle is:

The equation of the base of an equilateral triangle is $x+y=2$ and its opposite vertex is $(2,1)$. If $m_1, m_2$ are the slopes of the other two sides and the length of its side is $a$,then $|m_1-m_2|+a \sqrt{2}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module