Straight Lines ...

An aeroplane flying horizontally $$1$$, above the ground is observed at an elevation of $$60$$ and after $$10$$ seconds the elevation is observed to be $$30$$. The uniform speed of the aeroplane in $$/h$$ is-

Points $$A(\sqrt{2}, 4)$$, $$B(6, \sqrt{3})$$ and C are collinear. If B is the midpoint of line segment AC, approximately calculate the (x, y) coordinates of point C.

A straight line L through the point $$(3,-2)$$ is inclined at an angle $$60$$ to the line $$\sqrt { 3 } x+y=1$$. If L also intersects the x-axis, the equation of L is-

A straight line is drawn through the point $$p\ (2,3)$$ and is inclined at an angle of $$30^{o}$$ with the $$x-$$axis, the co-ordinates of two points on it at a distance of $$4$$ from $$p$$ is/are

If the vertices of a triangle are $$(1,2),(4,-6)$$ and $$(3,5)$$, then its area is

The points given are $$(1, 1)$$, $$(-2, 7)$$ and $$(3, 3)$$.Find distance between the points.

The points $$(a, b), (-a, -b), (b\sqrt{3}, -a\sqrt{3})$$ are the vertices of a triangle which is

A line passing through $$(3,4)$$ meets the axis $$\overline {OX} $$ and $$\overline {OY} $$ at $$A$$ and $$B$$ respectively. Find the minimum area of triangle OAB. 

The intercepts on the straight $$y=mx$$ by the line $$y=2$$ and $$y=6$$ is less than $$5$$, then $$m$$ belongs to

$$ABC$$ is an isosceles triangle. If the coordinates of the base are $$B(1,3)$$ and $$C(-2,7)$$, the coordinates of vertex $$A$$ can be