Fast way to do this problem?

[deeps005]

Advertisement - Members don't see this ad

I know how to do this problem but my method takes forever....there has to be a faster way to do it:

you have 3 points with cordinates A =(3,-6), B=(1,1), and C=(7,6). What is the area of the triangle ABC?

I first found the equation of the line that's perpindicular to AC that goes through B. Then I figured out where the perpindicular line intersects AC, lets call that point D. Then found the distance between point B and D. That gave me the height of the triangle. Then I found the length of the line AC which gave me the base of the triangle.

I know my method works but is there a shortcut?

 

[Balki]

Another way to do the problem would be to use Heron's formula that give you the area of a trianlge using only 3 sides

A= sqrt(S(S-a)(S-b)(S-c) )

Where S = 1/2 of Perimeter. and a, b, c are the sides. You'll find the sides using the distance equation.

But this turns out to be a nightmare to calculte. However, sometimes this formula can be quite useful.
Does anyone else have suggestions?