Question

A(4, 2), B(6, 5) and C(1, 4) are the vertices of ΔABC.

(i) The median from A meets BC in D. Find the coordinates of the point D.

(ii) Find the coordinates of point P on AD such that AP : PD = 2 : 1.

(iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : l and CR : RF= 2 : 1.

(iv) What do you observe?

Answer 1

(i) Median AD of the triangle will divide the side BC in two equals parts. So D is themidpoint of side B.

Coordinates of D

(ii) Point P divides the side AD in a ratio 2:1

Coordinates of P

(iii) Median BE of the triangle will divide the side AC in two equal parts. So E is the midpoint 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. So F is the midpoint of side AB.

(iv) Now we may observe that coordinates of point P, Q, R are same. So, all these are representing same point on the plane i.e. centroid of the triangle.