The area of the triangle formed by the points | 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 $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) The area of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ 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 points $(a, b + c)$,$(b, c + a)$,and $(c, a + b)$:Area $= \frac{1}{2} |a(c + a - a - b) + b(a + b - b - c) + c(b + c - c - a)|$$= \frac{1}{2} |a(c - b) + b(a - c) + c(b - a)|$$= \frac{1}{2} |ac - ab + ba - bc + cb - ca|$$= \frac{1}{2} |0| = 0$.Since the area is $0$,the points are collinear.

The area of the triangle formed by the points $(a, b + c)$,$(b, c + a)$,and $(c, a + b)$ is equal to:

Similar Questions

Which of the following is the closest relative of humans?

If $(h, k)$ is the image of the point $(2, -3)$ with respect to the line $5x - 3y = 2$,then $h + k$ is equal to

If $X = \{ 4^n - 3n - 1 : n \in N \}$ and $Y = \{ 9(n - 1) : n \in N \}$,then $X \cup Y$ is equal to

The world's most problematic aquatic weed is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module