Find the area of the triangle ABC with vertex | vedclass

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

Question

(D) Let the coordinates of vertices $B$ and $C$ be $(a, b)$ and $(x, y)$ respectively.The mid-point of side $AB$ is given as $(2, -1)$. Thus,$\left(\f

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(D) Let the coordinates of vertices $B$ and $C$ be $(a, b)$ and $(x, y)$ respectively.The mid-point of side $AB$ is given as $(2, -1)$. Thus,$\left(\frac{1+a}{2}, \frac{-4+b}{2}ight) = (2, -1)$.Equating the coordinates,we get $1+a = 4 \implies a = 3$ and $-4+b = -2 \implies b = 2$. So,$B = (3, 2)$.The mid-point of side $AC$ is given as $(0, -1)$. Thus,$\left(\frac{1+x}{2}, \frac{-4+y}{2}ight) = (0, -1)$.Equating the coordinates,we get $1+x = 0 \implies x = -1$ and $-4+y = -2 \implies y = 2$. So,$C = (-1, 2)$.The vertices of $	riangle ABC$ are $A(1, -4)$,$B(3, 2)$,and $C(-1, 2)$.The area of $	riangle ABC = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$.Area $= \frac{1}{2} |1(2 - 2) + 3(2 - (-4)) + (-1)(-4 - 2)|$.Area $= \frac{1}{2} |0 + 3(6) - 1(-6)| = \frac{1}{2} |18 + 6| = \frac{24}{2} = 12$ $sq. units$.

Find the area of the triangle $ABC$ with vertex $A (1, -4)$ and the mid-points of the sides passing through $A$ being $(2, -1)$ and $(0, -1)$ (in $sq. units$).

Similar Questions

If three vertices of a parallelogram $ABCD$ are $A(3,2)$,$B(4,5)$,and $C(2,3)$,then find the coordinates of the fourth vertex $D$.

$\overline{AB}$ is a diameter of a circle having the centre $P$. If $A(5, -6)$ and $B(3, -2)$,then the coordinates of $P = \dots$

The area of a triangle with vertices $A (3,0), B (7,0)$ and $C (8,4)$ is

For $A(0, 0)$ and $B(4, 8)$,$M$ is the midpoint of $\overline{AB}$ and $N$ is the midpoint of $\overline{BM}$,then the coordinates of $N$ are.........

The line segment joining $(0,0)$ and $(6,6)$ is divided into four congruent parts. Which of the following is one of the dividing points?

Vedclass Test Series

Exam Paper Generator

Online Exam Module