Straight Lines ...

Find the value of $$x$$ such that $$AB=BC$$ where the coordinates of A, B and C are $$(2,1)$$, $$(x,0)$$  and $$(-2,-1)$$ respectively.

The condition that the slope of one of the lines represented by $$ax^{2} + 2hxy + by^{2} = 0$$ is twice that of the other is

If $$(3,2)$$ and $$(-3,2)$$ are two vertices of an equilateral triangle which contains within it the origin, what are the coordinates of the third vertex ?

If $$A(a,a), B(-a,-a)$$ are two vertices of an equilateral triangle, then its third vertex is

The coordinates of the point which divides the line segment joining points $$A(0 , 0)$$ and $$B(9 , 12)$$ in the ration $$1 : 2$$ are 

The ratio in which xy-plane divides the line segment joining $$(2,4,5)$$ and $$(3,5,-4)$$ is

Find the value of $$x_i$$, if the distance between the points $$(x_i, 2)$$ and $$(3, 4)$$ is $$8$$.

The coordinates of a point on Y-axis which are at a distance of $$5\sqrt 2 $$ from the point $$P(3,-2,5)$$ is -

Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are $$(0.-1), (2, 1) and (0, 3)$$

C is a point on the line segment joining A(-3, 4) and B (2, 1) such that AC = 2 BC then coordinates of C are