The point $P(3,6)$ is first reflected on the line $y=x$ and then the image point $Q$ is again reflected on the line $y=-x$ to get the image point $Q^{\prime}$. Then, the circumcentre of the $\Delta P Q Q^{\prime}$ is

If a pair of perpendicular lines through the origin together with the straight line $2x + 3y = 6$ form an isosceles triangle,then the area of that triangle (in sq units) is

If the vertices of a triangle have integer coordinates,then what type of triangle can it never be?

Without using the distance formula,show that the points $(-2,-1), (4,0), (3,3),$ and $(-3,2)$ are the vertices of a parallelogram.

Let $ABC$ be a triangle and $M$ be a point on side $AC$ closer to vertex $C$ than $A$. Let $N$ be a point on side $AB$ such that $MN$ is parallel to $BC$ and let $P$ be a point on side $BC$ such that $MP$ is parallel to $AB$. If the area of the quadrilateral $BNMP$ is equal to $\frac{5}{18}$ of the area of $\triangle ABC$,then the ratio $AM/MC$ equals

The quadrilateral formed by the vertices $A(-1, 1)$,$B(0, -3)$,$C(5, 2)$,and $D(4, 6)$ is: