If A(4,9), B(2,3), and C(6,5) are the vertices of ∆ABC, then the length of the median through C is
(a) 5 units
(b) √10 units
(c) √25 units
(d) 10 units
It is given that A(4,9), B(2,3), and C(6,5) are the vertices of ∆ABC.
Let CD be the median of ∆ABC through C. Then, D is the mid-point of AB.
Using mid-point formula, coordinates of midpoint =(x1+x22,y1+y22), we get
Here, Taking A(x1,y1) and B(x2,y2) points, x1=4, x2=2, y1=9, y2=3
Coordinates of D =(x1+x22,y1+y22)=(4+22,9+32)
=(62,122)=(3,6)
Using distance formula, Length between two points =√(x2−x1)2+(y2−y1)2
Here,Taking A(x1,y1) and D(x2,y2) points, x1=4, x2=3, y1=9, y2=6
Length of the median, AD =√(x2−x1)2+(y2−y1)2
=√(3−4)2+(6−9)2
=√(−1)2+(−3)2
=√10 units
Thus, the length of the required median is √10 units.
Hence, the correct answer is option B.