the points c and d are on the line segment joining A(-4,7) and B(5,13) such that AC=CD=DB.Then find co-ordinates of points C and D
Answers
Co-ordinates of C = ( -1 , 9) & Co-ordinates of D = (2 , 11)
Step-by-step explanation:
AC = CD = DB = R
AC + CD + DB = AB
=> R + R + R = AB
=> AB = 3R
AC = R
BC = AB - AC = 3R - R = 2R
=> AC : BC :: R : 2R
=> AC : BC :: 1 : 2
A (-4 , 7) & B ( 5 , 13)
C Divides AB in 1 : 2 Ratio
Coordinates of C are = (1 * 5 + 2*(-4))/(1 + 2) , (1 * 13 + 2 * 7)/(1 + 2)
= ( -3/3 , 27/3)
= - 1 , 9
Co-ordinates of C = ( -1 , 9)
CD = DB = R
=> D Divides CB in 1:1 Ratio
C = (-1, 9) B = (5 , 13)
Co-ordinates of D = ( -1 + 5)/2 . (9 + 13)/2 = 2 , 11
A -4 , 7
C -1 , 9
D 2 , 11
B 5 , 13
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