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Question

The points (6, 6), (0, 6) and (6, 0) are the vertices of a right triangle as shown in the figure. Find the distance between its centroid and D (point of median of AB).



A

3 units

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B

6 units

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C

2units

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D

5units

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Solution

The correct option is C

2units


Point D = midpoint of AB
=(x1+x22,y1+y22)
=(6+02, 6+02)=(3,3)

Centroid (G) =(x1+x2+x33, y1+y2+y33)=(6+0+63, 0+6+63)=(4,4)

Distance between two points (x1,y1) and (x2,y2) is (x2x1)2+(y2y1)2Distance between centroid and pointof median AB=(43)2+(43)2 =1+1 =2 units


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