The four points whose co-ordinates are $(2, 1), (1, 4), (4, 5), (5, 2)$ form :
a rectangle which is not a square
a trapezium which is not a parallelogram
a square
a rhombus which is not a square.
The area of triangle formed by the lines $x = 0,y = 0$ and $\frac{x}{a} + \frac{y}{b} = 1$, is
The diagonals of the parallelogram whose sides are $lx + my + n = 0,$ $lx + my + n' = 0$,$mx + ly + n = 0$, $mx + ly + n' = 0$ include an angle
Let $m, n$ be real numbers such that $0 \leq m \leq \sqrt{3}$ and $-\sqrt{3} \leq n \leq 0$. The minimum possible area of the region of the plane consisting of points $(x, y)$ satisfying in inequalities $y \geq 0, y-3 \leq m x$, $y -3 \leq nx$, is
The equation of base $BC$ of an equilateral triangle is $3x + 4y = 1$ and vertex is $(-3,2),$ then the area of triangle is-
The co-ordinates of three points $A(-4, 0) ; B(2, 1)$ and $C(3, 1)$ determine the vertices of an equilateral trapezium $ABCD$ . The co-ordinates of the vertex $D$ are :