The sides of a triangle are $3x+2y-6=0$,$2x-3y+6=0$,and $x+2y+2=0$. If $P(0, b)$ lies either on the triangle or inside the triangle,then $b$ lies in the interval

$A$ triangle $ABC$ lying in the first quadrant has two vertices as $A(1, 2)$ and $B(3, 1)$. If $\angle BAC = 90^{\circ}$ and $\text{ar}(\Delta ABC) = 5\sqrt{5}$ sq. units,then the abscissa of the vertex $C$ is

Two adjacent sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. If the equation of one diagonal is $11x + 7y - 9 = 0$,find the equation of the other diagonal.

The vertices of a triangle are $(2, 1)$,$(5, 2)$ and $(4, 4)$. The lengths of the perpendiculars from these vertices to the opposite sides are

The sides of a $\triangle ABC$ are positive integers. The smallest side has length $1$. Which of the following statements is true?

The vertex of the right angle of a right-angled triangle lies on the straight line $2x + y - 10 = 0$. If the two other vertices are at points $(2, -3)$ and $(4, 1)$,then the area of the triangle in sq. units is: