In a triangle ABC bisector of angle BAC meets BC at D.A,B,C have co-ordinates (0,0), (3, 4) and (-6,8) respectively then length of is equal to
Answers
Given : ABC bisector of angle BAC meets BC at D. A,B,C have co-ordinates (0,0), (3, 4) and (-6,8) respectively
To Find : Length of AD
Solution:
bisector of angle BAC meets BC at D
A (0,0),
B (3, 4)
C (-6,8)
bisector of angle BAC meets BC at D
=> AC / AB = CD/ BD
AC = √(0 -(-6))² + (0-8)² = √36 + 64 = 10
AB = 5
AC/AB = 10/5 = 2/1 = 2 :1
CD/BD = 2 : 1 => D bisect CB in 2 : 1 ratio
C (-6,8) B (3, 4)
D = ( 2 * 3 + 1(-6))/( 2 + 1) , ( 2 * 4 + 1 * 8)/(2 + 1)
=> D = 0 , 16/3
A = ( 0 , 0) D = ( 0, 16/3)
Length of AD = 16/3
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