If the line $3x + 4y - 24 = 0$ 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

The length of the altitude through $A$ of the triangle $ABC$,where $A \equiv (-3, 0)$,$B \equiv (4, -1)$,and $C \equiv (5, 2)$,is

The points $(1,3)$ and $(5,1)$ are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line $y=2x+c$,then one of the vertices on the other diagonal is

If $ad-bc \neq 0$,then the area (in sq. units) of the parallelogram formed by the lines $ax+by+2=0$,$ax+by+5=0$,$cx+dy+3=0$ and $cx+dy+7=0$ is

Let $ABCD$ be a square and let $P$ be a point on segment $CD$ such that $DP:PC=1:2$. Let $Q$ be a point on segment $AP$ such that $\angle BQP=90^{\circ}$. Then,the ratio of the area of quadrilateral $PQBC$ to the area of the square $ABCD$ is

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