If vertices of a quadrilateral are $A(0,0), B(3,4), C(7,7)$ and $D(4,3)$,then the quadrilateral $ABCD$ is

If two vertices of an equilateral triangle are $(1, 0)$ and $(3, 0)$,and the third vertex lies in the first quadrant,find the area of the triangle.

Three points are $A(6, 3)$,$B(-3, 5)$,and $C(4, -2)$. If $P(x, y)$ is a point,then the ratio of the area of $\Delta PBC$ to the area of $\Delta ABC$ is:

The coordinates of three points $A(-4, 0)$,$B(2, 1)$,and $C(3, 1)$ determine the vertices of an isosceles trapezium $ABCD$. The coordinates of the vertex $D$ are:

If $x_1, x_2, x_3$ and $y_1, y_2, y_3$ are in $G.P.$ with the same common ratio,then the points $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ are:

Let the equations of two adjacent sides of a parallelogram $ABCD$ be $2x - 3y = -23$ and $5x + 4y = 23$. If the equation of its one diagonal $AC$ is $3x + 7y = 23$ and the distance of $A$ from the other diagonal is $d$,then $50d^2$ is equal to $........$.