The area of a triangle whose vertices are (a | vedclass

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

Question

(D) The area of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is given by $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_

Vedclass · Accepted Answer

$ab$

Vedclass · Answer

(D) The area of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is given by $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$.Substituting the given vertices:$x_1 = a \cos 	heta, y_1 = b \sin 	heta$$x_2 = -a \sin 	heta, y_2 = b \cos 	heta$$x_3 = -a \cos 	heta, y_3 = -b \sin 	heta$Area $= \frac{1}{2} |a \cos 	heta (b \cos 	heta - (-b \sin 	heta)) + (-a \sin 	heta)(-b \sin 	heta - b \sin 	heta) + (-a \cos 	heta)(b \sin 	heta - b \cos 	heta)|$$= \frac{1}{2} |a \cos 	heta (b \cos 	heta + b \sin 	heta) - a \sin 	heta (-2b \sin 	heta) - a \cos 	heta (b \sin 	heta - b \cos 	heta)|$$= \frac{ab}{2} |\cos^2 	heta + \cos 	heta \sin 	heta + 2 \sin^2 	heta - \sin 	heta \cos 	heta + \cos^2 	heta|$$= \frac{ab}{2} |2 \cos^2 	heta + 2 \sin^2 	heta|$$= \frac{ab}{2} 	imes 2(\cos^2 	heta + \sin^2 	heta) = ab(1) = ab$.

The area of a triangle whose vertices are $(a \cos \theta, b \sin \theta)$,$(-a \sin \theta, b \cos \theta)$,and $(-a \cos \theta, -b \sin \theta)$ is:

Similar Questions

If $(1, 1)$,$(3, 4)$,$(5, -2)$,and $(4, -7)$ are the vertices of a quadrilateral,find its area.

The area enclosed by the curve $|x + y| + |x - y| = 11$ is

$A$ triangular corner is cut from a rectangular piece of paper and the resulting pentagon has sides $5, 6, 8, 9, 12$ in some order. The ratio of the area of the pentagon to the area of the rectangle is

The vertices of the triangle $ABC$ are $(2, 1)$,$(4, 3)$,and $(2, 5)$. If $D$,$E$,and $F$ are the mid-points of the sides,then the area of the triangle $DEF$ is:

Find the area of a triangle given that midpoints of its sides are $(2, 7)$, $(1, 1)$, and $(10, 8)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module