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CBSE Class 10 Answered

Find the centroid of a triangle whose vertices are (x1,y1), (x2,y2), (x3,y3).
Asked by Topperlearning User | 26 Sep, 2017, 13:59: PM
answered-by-expert Expert Answer

Let A(x1,y1), B(x2,y2), C(x3,y3).
Let D be the mid point of AB
By mid point formula coordinates of D will be begin mathsize 12px style open parentheses fraction numerator straight x subscript 1 space plus space straight x subscript 2 over denominator 2 end fraction comma fraction numerator straight y subscript 1 space plus space straight y subscript 2 over denominator 2 end fraction close parentheses end style
Now the centroid of the triangle divides the medians in the ratio 2:1.
Applying the section formula to get the co-ordinates of centroid, point P(x,y) on CD
Co-ordinates of P are
begin mathsize 12px style straight x space equals space fraction numerator 1 cross times straight x subscript 2 space plus space 2 open parentheses begin display style fraction numerator straight x subscript 1 space plus space straight x subscript 2 over denominator 2 end fraction end style close parentheses over denominator 1 space plus space 2 end fraction equals fraction numerator straight x subscript 1 space plus space straight x subscript 2 space plus space straight x subscript 3 over denominator 3 end fraction end style
Error converting from MathML to accessible text.
The centroid of the triangle is
Answered by | 26 Sep, 2017, 15:59: PM

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