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?

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.

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) – [4.5 + 15 + 12] = 16.5 sq units

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.)

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

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.

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