(a) Explanation Formula used: 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 Midpoint Formula: The midpoint M = ( x , y ) of the line segment from P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) is, M = ( x , y ) = ( x 1 + x 2 2 , y 1 + y 2 2 ) . Calculation: In order to find the midpoint of the shortest side, first find the length of the shortest distance. Consider the given the points as A = ( 1.4 , 1.3 ) , B = ( 2.6 , 1.5 ) and C = ( 2.7 , 1.7 ) . Compute the length of the side AB of the triangle as follows. Consider the points A = ( 1.4 , 1.3 ) and B = ( 2.6 , 1.5 ) Here, x 1 = 1.4 , y 1 = 1.3 and x 2 = 2.3 , y 2 = 1.5 . Substitute x 1 = 1.4 , y 1 = 1.3 and x 2 = 2.3 , y 2 = 1.5 in the distance formula d ( P 1 , P 2 ) = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 and simplify as follows. d ( A , B ) = ( 2.3 − 1.4 ) 2 + ( 1.5 − 1.3 ) 2 = ( 0.9 ) 2 + ( 0.2 ) 2 = 0.81 + 0.04 = 0.85 = 0.92 That is, d ( A , B ) = 0.92 . Compute the length of the side BC of the triangle as follows. Consider the points B = ( 2.6 , 1.5 ) and C = ( 2.7 , 1.7 ) . Here, x 1 = 2.6 , y 1 = 1.5 and x 2 = 2.7 , y 2 = 1.7 . Substitute x 1 = 2.6 , y 1 = 1.5 and x 2 = 2.7 , y 2 = 1.7 in the distance formula d ( P 1 , P 2 ) = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 and simplify as follows (b) To determine The length of the median for the midpoint obtained in part (a).

College Algebra: Concepts Through Functions (4th Edition)

4th Edition

ISBN: 9780134686967

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Chapter F.1, Problem 67AYU

(a)

To determine

The midpoint of the shortest side.

(b)

To determine

The length of the median for the midpoint obtained in part (a).

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Chapter F.1, Problem 66AYU

Chapter F.1, Problem 68AYU

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College Algebra: Concepts Through Functions (4th Edition)

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