Straight Lines ...

A vertical line $$l$$ passes through the point $$(2,3)$$. A horizontal line $$m$$ passes through the point $$(-1,6)$$. Where do lines $$l$$ and $$m$$ intersect?

In which adjacent figures, the path is the shortest path?

The line $$\displaystyle 3x+2y=24$$ meets x-axis at A and y-axis at B. The perpendicular bisector of $$\displaystyle \overline { AB } $$ meets the line through (0, -1) and parallel to x-axis at C. Find the area of $$\displaystyle \Delta ABC$$.

Area of the regular hexagon whose diagonal is the join of $$\left( 2,4 \right)$$ and $$\left( 6,7 \right)$$ is

An equilateral triangle has one vertex at $$(3, 4)$$ and another at $$(-2, 3) $$. Find the coordinates of the third vertex.

If the area of the triangle whose vertices are $$(b,c),(c,a)$$ and $$(a,b)$$ is $$\triangle$$, then the area of the triangle whose vertices are $$(ac-{b}^{2},ab-{c}^{2}),(ab-{c}^{2},bc-{a}^{2}) and $$(cb-{a}^{2},ca-{b}^{2})$$ is

What is the angle between the straight lines $$\left( { m }^{ 2 }-mn \right) y=\left( mn+{ n }^{ 2 } \right) x+{ n }^{ 3 }$$ and $$\left( mn+{ m }^{ 2 } \right) y=\left( mn-{ n }^{ 2 } \right) x+{ m }^{ 3 }$$, where $$m> n$$?

The line through point $$(m, -9)$$ and $$(7, m)$$ has slope m. The y-intercept of this line, is?

The area of the triangle formed by the positive $$x -$$axis, and the normal and tangent to the circle $${x}^{2}+{y}^{2}=4$$ at $$(1,\ \sqrt{3})$$ is

The points A $$(2a, 4a)$$, B $$(2a, 6a)$$ and C$$(2a+\sqrt{3a}, 5a)$$ (when $$a > 0$$) are vertices of?