Hello, SaRah<3!

Here's #1 . . . in baby steps . . .

1. The vertices of a right triangle are A(3,3), B(-1,4), and C(1,-5).

Find the area of the triangle.

A sketch is always a good idea . . . Code:

(-1,4)
B o |
* |
*
* | *
| *
* | *
| *
*| *
| o A
* * (3,3)
- - - + - - - * - - -
|* *
| *
| o
| C (1,-5)

Even a rough sketch makes us suspect that:

We find that: .

. . and that: .

Since the slopes are negative reciprocals of each other:

The base of the triangle is: .

The height of the triangle is: .

The area of a triangle is: .

. . so we have: . square units.

Edit: EB's too fast for me . . . and with a shorter solution!