2. Lesson #7: Application of Determinants
Accel Precalc
Unit #3: Matrices
Lesson #7: Application of Determinants
EQ: How can you use determinants of matrices to find area of triangles?

3. Consider a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3).
Area of a Triangle
Consider a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3).
If the triangle was a right triangle, how would we compute the area of the triangle? A = _______
When the triangle is not a right triangle, we must use other ways to find the area.

4. Geometric Technique:
The triangle can be enclosed in a rectangle.
The vertices of the triangle will
intersect the rectangle in three
places, forming three right triangles.
These triangles are denoted A, B, and C.
A = _________
B = __________
Find the area of each right triangle:
C = _________
How can you use these values to find the area of the triangle?
Area Rec – [Area Tri A + Area Tri B + Area Tri C]
(8)(6) – [ ] = 16.5 sq units

5. How do you find the determinant of a 3 x 3 matrix?
Using Determinants:
Formula for the area of a triangle using determinants:
RECALL:
How do you find the determinant of a 3 x 3 matrix?
Use this formula to find the area of the given triangle.
(I will travel left-to-right, clockwise, around the triangle.)

6. How do you find the determinant of a 3 x 3 matrix?
RECALL PREVIOUS LESSON!

7. Area MUST ALWAYS be positive!!
How do you know whether to use + or - ?
Area MUST ALWAYS be positive!!
If determinant is + , use +1/2.
if determinant is -, use -1/2.

8. Worksheet Finding Area of Triangles Using Determinants
Assignment :
Worksheet Finding Area of Triangles Using Determinants