Explanation Formula used: The mid-point of the line segment P 1 ( x 1 , x 2 ) and P 2 ( x 2 , y 2 ) is ( x 1 + x 2 2 , y 1 + y 2 2 ) . The distance between two points P 1 ( x 1 , x 2 ) and P 2 ( x 2 , y 2 ) is given by d = | P 1 P 2 | = ( x 2 − x 1 ) 2 − ( y 2 − y 1 ) 2 . Calculation: Let the triangle whose vertices be A ( 1 , 0 ) , B ( 3 , 6 ) and C ( 8 , 2 ) . The rough graph of the triangle with vertices A ( 1 , 0 ) , B ( 3 , 6 ) and C ( 8 , 2 ) and medians is shown below in Figure 1. From Figure 1, it is observed that the midpoints of AB, BC and CA are denoted as M 1 , M 2 and M 3 respectively and the medians are A M 2 . B M 3 and C M 1 . In order to find the lengths of the medians, find the midpoints of the vertices. Consider two points A ( 1 , 0 ) and B ( 3 , 6 ) , from that x 1 = 1 , y 1 = 3 , x 2 = 0 and y 2 = 6 . Find the midpoint of AB by using the above values as follows. M 1 = ( 1 + 3 2 , 0 + 6 2 ) = ( 4 2 , 6 2 ) M 1 = ( 2 , 3 ) Hence, the midpoint is M 1 = ( 2 , 3 ) . Consider two points B ( 3 , 6 ) and C ( 8 , 2 ) , from that x 1 = 3 , y 1 = 6 , x 2 = 8 and y 2 = 2 . Find the midpoint of BC by using the above values as follows. M 2 = ( 3 + 8 2 , 6 + 2 2 ) = ( 11 2 , 8 2 ) M 2 = ( 11 2 , 4 ) Hence, the midpoint is M 2 = ( 11 2 , 4 ) . Consider two points C ( 8 , 2 ) and A ( 1 , 0 ) , from that x 1 = 8 , y 1 = 2 , x 2 = 1 and y 2 = 0 . Find the midpoint of BC by using the above values as follows. M 3 = ( 8 + 1 2 , 2 + 0 2 ) = ( 9 2 , 2 2 ) M 3 = ( 9 2 , 1 ) Hence, the midpoint of is M 3 = ( 9 2 , 1 ) . Consider two points M 2 ( 11 2 , 4 ) and A ( 1 , 0 ) , from that x 1 = 11 2 , y 1 = 4 , x 2 = 1 and y 2 = 0

Single Variable Calculus: Early Transcendentals

8th Edition

ISBN: 9781305270336

Author: James Stewart

Publisher: Cengage Learning

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Chapter B, Problem 56E

To determine

To find: The lengths of the medians of the triangle with vertices A(1,0),B(3,6) and C(8,2).

Expert Solution & Answer

Chapter B Solutions

Single Variable Calculus: Early Transcendentals

Ch. B - Prob. 1E Ch. B - Prob. 2E Ch. B - Prob. 3E Ch. B - Prob. 4E Ch. B - Prob. 5E Ch. B - Prob. 6E Ch. B - Prob. 7E Ch. B - Prob. 8E Ch. B - Prob. 9E Ch. B - Prob. 10E

Ch. B - Show that the triangle with vertices A(0, 2), B(3,...Ch. B - (a) Show that the triangle with vertices A(6, 7),...Ch. B - Prob. 13E Ch. B - (a) Show that the points A(1, 3), B(3, 11), and...Ch. B - Show that A(1, 1), B(7, 4), C(5, 10), and D(1, 7)...Ch. B - Prob. 16E Ch. B - Prob. 17E Ch. B - Prob. 18E Ch. B - Prob. 19E Ch. B - Prob. 20E Ch. B - Prob. 21E Ch. B - Prob. 22E Ch. B - Prob. 23E Ch. B - Prob. 24E Ch. B - Find an equation of the line that satisfies the...Ch. B - Prob. 26E Ch. B - Prob. 27E Ch. B - Prob. 28E Ch. B - Prob. 29E Ch. B - Find an equation of the line that satisfies the...Ch. B - Prob. 31E Ch. B - Prob. 32E Ch. B - Prob. 33E Ch. B - Prob. 34E Ch. B - Prob. 35E Ch. B - Prob. 36E Ch. B - Prob. 37E Ch. B - Prob. 38E Ch. B - Prob. 39E Ch. B - Prob. 40E Ch. B - Prob. 41E Ch. B - Prob. 42E Ch. B - Prob. 43E Ch. B - Prob. 44E Ch. B - Prob. 45E Ch. B - Prob. 46E Ch. B - Prob. 47E Ch. B - Prob. 48E Ch. B - Prob. 49E Ch. B - Prob. 50E Ch. B - Prob. 51E Ch. B - Prob. 52E Ch. B - Prob. 53E Ch. B - Prob. 54E Ch. B - Find the midpoint of the line segment joining the...Ch. B - Prob. 56E Ch. B - Prob. 57E Ch. B - Show that the lines 3x 5y + 19 = 0 and 10x + 6y ...Ch. B - Prob. 59E Ch. B - Prob. 60E Ch. B - Prob. 61E Ch. B - Prob. 62E

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