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(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What do yo observe?
[Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2 : 1.]
(v) If and
are the vertices of
, find the coordinates of the centroid of the triangle.
Asked by Ankit Last Modified
Answer 
Tasneem
(i) Median AD of the triangle will divide the side BC in two equal parts.
Therefore, D is the mid-point of side BC.
(ii) Point P divides the side AD in a ratio 2:1.
(iii) Median BE of the triangle will divide the side AC in two equal parts.
Therefore, E is the mid-point of side AC.
Point Q divides the side BE in a ratio 2:1.
Median CF of the triangle will divide the side AB in two equal parts. Therefore, F is the mid-point of side AB.
Point R divides the side CF in a ratio 2:1.
(iv) It can be observed that the coordinates of point P, Q, R are the same.
Therefore, all these are representing the same point on the plane i.e., the centroid of the triangle.
(v) Consider a triangle, ΔABC, having its vertices as A(x1, y1), B(x2, y2), and C(x3,
y3).
Median AD of the triangle will divide the side BC in two equal parts. Therefore, D is the mid-point of side BC.
Let the centroid of this triangle be O.
Point O divides the side AD in a ratio 2:1.
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