If the area of the triangle having the vertic | vedclass

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

Question

(C) 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

$a = 9$ or $a = -1$

Vedclass · Answer

(C) 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 $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Given vertices are $A(a, 5), B(6, 7),$ and $C(2, 3)$ with Area $= 10$.Substituting the values into the formula:$10 = \frac{1}{2} |a(7 - 3) + 6(3 - 5) + 2(5 - 7)|$$20 = |a(4) + 6(-2) + 2(-2)|$$20 = |4a - 12 - 4|$$20 = |4a - 16|$This implies two cases:Case $1$: $4a - 16 = 20 \implies 4a = 36 \implies a = 9$Case $2$: $4a - 16 = -20 \implies 4a = -4 \implies a = -1$Thus,the possible values for $a$ are $9$ or $-1$.

If the area of the triangle having the vertices $A (a, 5), B (6, 7), C (2, 3)$ is $10$,then find $a$.

Similar Questions

$\overline{CD}$ is parallel to the $Y$-axis and $C(4, -5)$,then the coordinates of $D$ are $\ldots \ldots \ldots$

The area of a triangle having vertices $A(3, 0)$,$B(0, 3)$,and $C(3, 3)$ is:

The coordinates of a point dividing the line segment joining $A(8, 10)$ and $B(4, 12)$ from $A$ in the ratio $1:1$ are......

If $(-4,3)$ and $(4,3)$ are two vertices of an equilateral triangle,find the coordinates of the third vertex,given that the origin lies in the interior of the triangle.

The distance of the point $P(2, 3)$ from the $x$-axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module