Question

Triangle ABC is formed by joining the mid-points of the sides of triangle PQR. Another triangle DEF is formed by joining the mid-points of triangle ABC. If coordinates of D, E and F are (4,5), (-1, 2) and (-1, 4) respectively, then coordinates
of centroid of triangle PQR is​

Answer 1

Given  : Triangle ABC is formed by joining the midpoints of sides of triangle PQR. Another Triangle DEF is formed by joining the midpoints of triangle ABC

the coordinates of the points D,E,F are (4,5), (-1,2), (-1,4)

To Find : coordinates of centroid of triangle PQR

Solution:

Let say coordinate of  ΔPQR are

(Px , Py ) , ( Qx, Qy) , (Rx , Ry)

Hence centroid is  = (Px + Qx + Rx)/3 , ( Py + Qy + Ry)/3

Triangle ABC is formed by joining the midpoints of sides of triangle PQR.

A = ( Px + Qx)/2 ,   (Py + Qy)/2

B = ( Rx + Qx)/2 ,   (Ry + Qy)/2

C =  ( Px + Rx)/2 ,   (Py + Ry)/2

Triangle DEF is formed by joining the midpoints of triangle ABC

D = ( ( Px + Qx +Rx + Qx )/4 ,  (Py + Qy+ Ry + Qy)/4

E =   ( ( Px + Rx +Rx + Qx )/4 ,  (Py + Ry+ Ry + Qy)/4

F  =  ( ( Px + Qx +Rx + Px )/4 ,  (Py + Qy+ Ry + Py)/4

Centroid of DEF  =  ( 4Px + 4Qx + 4Rx)/4*3  ,  ( 4Py + 4Qy + 4Ry)/4*3

= ( Px + Qx + Rx)/3  ,  ( Py + Qy + Ry)/3

=  centroid  of PQR

Centroid of DEF = ( 4 - 1 - 1)/3 , ( 5 + 2 + 4)/2

= (2/3  , 3)

coordinates of centroid of triangle PQR = (2/3  , 3)

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Answer 2

Answer:

hi bro just for your info

the above answer is correct  but the last step is wrong its 2/3,11/3

Step-by-step explanation: