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Question

ABC is a triangle with vertices A(-1,4),B(6,-2)&c(-2,4),D,E&Fare the points which divide each AB,BC&CA, internally in the ratio 3:1. Then, the centroid of DEF is


A

(3,6)

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B

(1,2)

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C

(4,8)

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D

(-3,6)

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E

None of the above

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Solution

The correct option is B

(1,2)


Explanation for the correct option:

Step 1. Finding coordinate of D,E&F.

Let (x1,y1),(x2,y2),&(x3,y3) be the coordinates of D,E&F.

Given that D,E&F divide AB,BC&CA internally in the ratio of 3:1

Using formulae to find the coordinate of D,E&F

x1=[3(6)-1(1)]4=174y1=[-2(3)+4(1)]4=-12x1=mX1+nX22y1=mY1+nY22

Similarly,

x2=0,y2=52x3=-54,y3=4

Step 2. Finding point of centroid.

Assume (x,y) be the centroid of the triangle.

Then,

x=(x1+x2+x33)y=(y1+y2+y33)

Now put all the value

Hence,

x=13[(174)+0+(-54)]=1y=13[(-12)+(52)+4]=2

Therefore, the coordinate of the centroid is (1,2).
Hence, the correct option is (B)


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