Coordinate Geom...

$$\triangle ABC$$ has vertices $$A(-11, 4), B(-3, 8)$$, and $$C(3, -10)$$. The coordinates of the center of the circle circumscribed about $$\triangle ABC$$ are

Define the $$x$$-coordinate of the midpoint between $$(-1,1)$$ and $$(4,1)$$ as $$m$$ and define the $$y$$-coordinate of the midpoint between $$(4,1)$$ and $$(4,3)$$ as $$n$$. What are the $$x$$- and $$y$$- coordinates of $$(m,n)$$?

The vertices of $$\triangle ABC$$ have coordinates $$A(-7, 3), B(-1, 0)$$, and $$C(-2, 8)$$. The coordinates of the center of the circumscribed circle are

The area of the triangle whose co-ordinates are $$(2012, 7), (2014, 7)$$ and $$(2014, a)$$ is $$1 \,sq$$ unit. The sum of possible values of $$a$$ is

If  $$A =  (-3,4) , B =(-1,-2) , C=(5,6) D= (x,-4) $$  are the vertices of a quadrilateral such that area triangle $$ABD= 2 \times$$ (area of a triangle $$ACD$$), then $$x =$$

If (5, 7, 10), (1, 9, 6) are the extremities of the hypotenuse of a right angled isosceles triangle, then the third vertex is

A line L passes through the points $$ (1,1)  $$and $$ (2,0)  $$ and another line $$  L^{\prime}  $$ passes through $$ \left(\frac{1}{2}, 0\right)  $$ and perpendicular to L.Then the area of the triangle formed by the lines $$  L, L^{\prime}  $$ and $$  y- $$ axis, is

The area of the triangle formed by the lines $$x=0;y=0$$ and $$x\sin { { 18 }^{ 0 } } +y\cos { { 36 }^{ 0 } } +1=0$$ is 

One diagonal of a square is along the line $$8x-15y=0$$ and one of its vertex is $$(1,2)$$. Then the equations of the sides of the square passing through this vertex, are

if the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then ---- test question