Explanation Formula used: The Distance formula : The distance between two points P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) , denoted by d ( P 1 , P 2 ) is d ( P 1 , P 2 ) = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . Calculation: It is known that, the Pythagorean theorem can be applied for only the right triangle . By the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the two sides of a right triangle. Find the distance between any two points P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) as follows. Locate any points P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) on the coordinate plane as shown below in Figure 1. Plot a line parallel to the y -axis through the point P 1 and a line parallel to the x -axis through the point P 2 such that these lines meet at the point ( x 1 , y 2 ) . The path traced by the points P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) forms a right triangle

4th Edition

ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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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°).

Chapter 12.1, Problem 49E

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To explain: How the distance formula is related to the Pythagorean Theorem.

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Chapter 12.1, Problem 48E

Chapter 12.1, Problem 50E

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Chapter 12 Solutions

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How the distance formula is related to the Pythagorean Theorem.

Solution Summary: The author explains how the distance formula is related to the Pythagorean Theorem.

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