↝ Median is a line segment drawn from the vertex to bisects the opposite sides and medians divides each other in the ratio 2 : 1.
Since,
It is given that,
↝ In triangle ABC,
Coordinates of vertex A = (2, 3)
and
Coordinates of D = (1, - 2),
where D is the midpoint of BC.
So,
↝ It implies AD is median of triangle ABC.
↝ Let assume that Centroid of a triangle be 'G' having coordinates (x, y).
Now,
↝ G divides AD in the ratio 2 : 1.
We know,
Section Formula is used to find the coordinates of the point (x, y) which divides the line segment joining the points A and B in the ratio m : n internally, and coordinates of C is given by
Answers & Comments
Verified answer
We know,
↝ Median is a line segment drawn from the vertex to bisects the opposite sides and medians divides each other in the ratio 2 : 1.
Since,
It is given that,
↝ In triangle ABC,
and
So,
↝ It implies AD is median of triangle ABC.
↝ Let assume that Centroid of a triangle be 'G' having coordinates (x, y).
Now,
↝ G divides AD in the ratio 2 : 1.
We know,
Section Formula is used to find the coordinates of the point (x, y) which divides the line segment joining the points A and B in the ratio m : n internally, and coordinates of C is given by
So, According to given data, we have
So, on substituting the values we get
Hence,
Coordinates of Centroid G (x, y) is
Additional Information :-
Distance Formula :-
Midpoint Formula :-
Area of triangle :-
Condition for 3 points to be collinear