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 . . .
B o |
* | *
* | *
| o A
* * (3,3)
- - - + - - - * - - -
| 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!