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Question

# 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

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Solution

## 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 getHere, Taking A(x1,y1) and B(x2,y2) points, x1=4, x2=2, y1=9, y2=3Coordinates 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)2Here,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 unitsThus, the length of the required median is √10 units.Hence, the correct answer is option B.

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