Question

In ∆ABC G is centriod if coordinates A are (x1 y1) and D are (x2 y2) find solution to find coordinate of G​

Answer 1

Answer:

Step-by-step explanation:

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