Question 4 If A (4, 9), B (2, 3) and C (6, 5) are the vertices of ∆ ABC, then the length of median through C is (A) 5 units (B) √10 units (C) 25 units (D) 10
Joining vertex C to line AB such that
CD is the median
Coordinates of D = Coordinates of Mid point of AB
= ((4 + 2)/2,(9 + 3)/2)
=((6 )/2,12/2)
= (3, 6)
Finding length of CD
Length of CD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √((3−6)2+(6−5)2)
= √((−3)2+12)
= √(9+1)
= √𝟏𝟎 units
So, the correct answer is (B)
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