Purchase Solution

Matrix and triangle area

Not what you're looking for?

Ask Custom Question

Determinates

a) In the accompanying figure, the area of the triangle ABC can be expressed as

area ABC = area ADEC + area CEFB - area ADFB

Use this and the fact the area of a trapezoid equals 1/2 the altitude times the sum of the parallel sides to show that:

(see attached filed)

Note: In the derivation of this formula, the vertices are labeled such that the triangle is traced coutnerclockwise proceeding from (x1, y1) to (x2, y2) to (x3, y3). For a clockwise orientation, the determinant above yields the negative of the area.

b) Use the result in (a) to find the triangle with vertices (3, 3), (4, 0), (-2, -1).

Attachments
Purchase this Solution

Solution Summary

This shows how to use a matrix to find the area of a triangle. The areas of a trapezoid at altitude times the sum of the parallel sides to show functions are determined.

Solution Preview

Area ABC = Area ADEC + Area CEFB - Area ADFB
Area ADEC = 1/2 (AD + EC)*DE = 1/2 (y1+y3)(x3 - x1)
Area CEFB = 1/2 (CE + FB)*EF = 1/2 (y3+y2)(x2 - x3)
Area ABDF = 1/2 (AD + BF)*DF = 1/2 (y1+y2)(x2 - ...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.