Find the area of the triangle formed by the p | vedclass

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

Question

(A) The area of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by the formula:Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) The area of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by the formula:Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Substituting the given coordinates $P(-1.5, 3)$,$Q(6, -2)$,and $R(-3, 4)$:Area $= \frac{1}{2} |-1.5(-2 - 4) + 6(4 - 3) + (-3)(3 - (-2))|$Area $= \frac{1}{2} |-1.5(-6) + 6(1) - 3(5)|$Area $= \frac{1}{2} |9 + 6 - 15|$Area $= \frac{1}{2} |0| = 0$ square units.Since the area is $0$,the points $P$,$Q$,and $R$ are collinear,meaning they lie on the same straight line and do not form a triangle.

Find the area of the triangle formed by the points $P(-1.5, 3)$,$Q(6, -2)$,and $R(-3, 4)$ (in square units).

Similar Questions

If the points $A (6, 1)$,$B (8, 2)$,$C (9, 4)$,and $D (p, 3)$ are the vertices of a parallelogram,taken in order,find the value of $p$.

Find the coordinates of a point $A,$ where $AB$ is the diameter of a circle whose centre is $(2,-3)$ and $B$ is $(1,4).$

If $Q(0, 1)$ is equidistant from $P(5, -3)$ and $R(x, 6)$,find the values of $x$. Also,find the distances $QR$ and $PR$.

Do the points $(3,2), (-2,-3)$ and $(2,3)$ form a triangle? If so,name the type of triangle formed.

$A$ median of a triangle divides it into two triangles of equal areas. Verify this result for $\Delta ABC$ whose vertices are $A (4, -6), B (3, -2)$ and $C (5, 2)$. Find the area of each triangle (in square units).

Vedclass Test Series

Exam Paper Generator

Online Exam Module