The line $3x + 2y = 24$ meets $y$-axis at $A$ and $x$-axis at $B$. The perpendicular bisector of $AB$ meets the line through $(0, - 1)$ parallel to $x$-axis at $C$. The area of the triangle $ABC$ is ............... $\mathrm{sq. \, units}$

  • A

    $182$

  • B

    $91$

  • C

    $48$

  • D

    None of these

Similar Questions

Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$, respectively. A right angled triangle $A M N$ is inscribed in the triangle $O A B$, where $O$ is the origin and the points $M$ and $N$ lie on the lines $OB$ and $A B$, respectively. If the area of the triangle AMN is $\frac{4}{9}$ of the area of the triangle $OAB$ and $AN : NB =\lambda: 1$, then the sum of all possible value$(s)$ of is $\lambda$ :

  • [JEE MAIN 2025]

If $A$ and $B$ are two points on the line $3x + 4y + 15 = 0$ such that $OA = OB = 9$ units, then the area of the triangle $OAB$ is

The equation of base $BC$ of an equilateral triangle is $3x + 4y = 1$ and vertex is $(-3,2),$ then the area of triangle is-

If the line $3x + 3y -24 = 0$ intersects the $x-$ axis at the point $A$ and the $y-$ axis at the point $B$, then the incentre of the triangle $OAB$, where $O$ is the origin, is

  • [JEE MAIN 2019]

The triangle formed by ${x^2} - 9{y^2} = 0$ and $x = 4$ is