# Geo3.8

From Example Problems

Show that the lines form an equilateral triangle with the line and find its area.

Given equation is

Let these two lines be respectively.

Let

Angle between L1,L2 is

Now or

Similarly,the angle between L1,L3 is

or

Therefore the three lines form a triangle.

Since the sum of the angles in any triangle is

Since the angles that we found are

Hence the three lines form an equilateral triangle.

Let p be the perpendicular distance from the vertex(0,0) to the line

Therefore,

Area of the triangle is units.