Explanation Given information : The triangle ABC has vertices A ( − 1 , 4 ) , B ( 3 , 2 ) a n d C ( 3 , − 6 ) . The midpoints of sides A B ¯ and A C ¯ given by M 1 a n d M 2 Formula Used: If we have two points ( x 1 , y 1 ) a n d ( x 2 , y 2 ) Midpoint formula (M) Slope formula(m) Distance formula (d) M = ( x 1 + x 2 2 , y 1 + y 2 2 ) m = y 2 − y 1 x 2 − x 1 d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Concept Involved: We need to create a triangle, label the vertices, and midpoints in order to visualize the problem. Calculation: Description Steps Find midpoint of side A B ¯ M 1 = ( − 1 + 3 2 , 4 + 2 2 ) = ( 2 2 , 6 2 ) = ( 1 , 3 ) Find midpoint of side A C ¯ M 2 = ( − 1 + 3 2 , 4 + − 6 2 ) = ( 2 2 , − 2 2 ) = ( 1 , − 1 ) Slope between the points M 1 and M 2 s l o p e o f M 1 M 2 ¯ = − 1 − 3 1 − 1 = − 4 0 { U n d e f i n e d S l o p e } Slope between the points B and C s l o p e o f B C ¯ = − 6 − 2 3 − 3 &

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 1, Problem 72SP

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ToShow : that the line segment M1M2¯ is parallel to side BC¯ , with half its length

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Chapter 1, Problem 71SP

Chapter 1, Problem 73SP

Chapter 1 Solutions

Calculus

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ToShow : that the line segment M 1 M 2 ¯ is parallel to side B C ¯ , with half its length

Solution Summary: The author explains how to create a triangle, label the vertices, and midpoints in order to visualize the problem.

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ToShow : that the line segment M1M2¯ is parallel to side BC¯ , with half its length

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Chapter 1 Solutions