Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

5th Edition

ISBN: 9781323132098

Author: Thomas, Lay

Publisher: PEARSON C

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Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Textbook Question

Chapter 3.3, Problem 30E

Let R be the triangle with vertices at (x₁, y₁), (x₂, y₂), and (x₃, y₃). Show that

{ area of triangle } = 1 2 det [ x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 ]

[Hint: Translate R to the origin by subtracting one of the vertices, and use Exercise 29.]

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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Chapter 3.3, Problem 29E

Chapter 3.3, Problem 31E

Chapter 3 Solutions

Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

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Let R be the triangle with vertices at ( x 1 , y 1 ), ( x 2 , y 2 ), and ( x 3 , y 3 ). Show that { area of triangle } = 1 2 det [ x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 ] [ Hint: Translate R to the origin by subtracting one of the vertices, and use Exercise 29.]

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