Let the midpoints of the sides of a triangle $ABC$ be $(\frac{5}{2}, 7)$, $(\frac{5}{2}, 3)$, and $(4, 5)$. If its incentre is $(h, k)$, then $3h + k$ is equal to:

If one side of an isosceles triangle is given by the line $y=2$ and the base is provided by the points $(2,0)$ and $(0,2)$,then its area (in sq. units) is

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

The equations of the sides $AB$,$BC$,and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 21a$ $(a \neq 0)$,and $x - y = 3$ respectively. Let $P(2, a)$ be the centroid of $\triangle ABC$. Then $(BC)^2$ is equal to $........$

If the incentre of the triangle formed by the lines $x-2=0$,$x+y-1=0$,and $x-y+3=0$ is $(\alpha, \beta)$,then $\beta=$

$7x+y-24=0$ and $x+7y-24=0$ represent the equal sides of an isosceles triangle. If the third side passes through $(-1, 1)$,then a possible equation for the third side is