SOLUTION: A right triangle is formed with vertices at the points (7,-2), (19,7), and (-5,14). What percent of the triangle's area lies in the fourth quadrant?

The part of triangle ABC that lies in the fourth quadrant
is the triangle DAE.

You find the area of triangle ABC by the determinant:



The area of triangle ABC is 300.

You must now find the area of triangle DAE

But to do that you must find the coordinates of D and E:

You find the equation of line CA by using the slope formula: 



and the point-slope formula 



and after doing that and simplifying, you get the equation 
of line CA, which is,
 
4x + 3y = 22 

Then point D is the x-intercept of line CA, so substitute 0 for y
and solve for x and get the coordinates of D as

 

Now exactly the same way, you'll find the equation of the line BE
as 

3x - 4y = 29

Then point E is the x-intercept of line BA, so substitute 0 for y
and solve for x and get the coordinates of E as



Then use the matrix method again to find the area of triangle DAE:



Finally you need to find what percent 25/3 is of 300.

So you divide 



So the area of triangle DAE is 1/36th of the area of triangle ABC.

To find out what percent that is, we multiply by 100%



Edwin