Explanation Given Information: The provided vertices of polygon are ( 4 , 0 ) , ( 2 , 1 ) and ( − 1 , − 5 ) . Formula used: If sum of the square of the length of two sides of a polygon are equal to square of the length of third side of a polygon, then the polygon is known as right triangle. a 2 + b 2 = c 2 Here, a and b are the length of two sides of right triangle and c is the length of hypotenuse of right triangle. Write the formula to find the distance between two points. d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Here, ( x 1 , y 1 ) and ( x 2 , y 2 ) are the two points in coordinate system. Proof: Draw the diagram for polygon from the provided data. From above diagram, calculate the distance between BC by use of distance formula, a = ( 4 − 2 ) 2 + ( 0 − 1 ) 2 = ( 2 ) 2 + ( − 1 ) 2 = 4 + 1 = 5 From above diagram, calculate the distance between AC by use of distance formula

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 8.1, Problem 8SWU

To determine

To prove: The provided points (4,0), (2,1) and (−1,−5) are the vertices of the right triangle.

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Chapter 8.1, Problem 7SWU

Chapter 8.1, Problem 9SWU

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Chapter 8 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 1SWU Ch. 8.1 - Prob. 2SWU Ch. 8.1 - Prob. 3SWU Ch. 8.1 - Prob. 4SWU Ch. 8.1 - Prob. 5SWU Ch. 8.1 - Prob. 6SWU

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To prove: The provided points ( 4 , 0 ) , ( 2 , 1 ) and ( − 1 , − 5 ) are the vertices of the right triangle.

Solution Summary: The author explains how the provided points are the vertices of the right triangle.

To prove: The provided points (4,0), (2,1) and (−1,−5) are the vertices of the right triangle.

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Chapter 8 Solutions