Question

1. The vertices of a triangle are (2,1), (-2,-2), (1,0). Then sum of squares of thelengths of the medians of the triangle is1. 25 2. 403. 30 4. 45​

Answer 1

30

Step-by-step explanation:

Assume the triangle be ABC.

Now, take, A =(2, 1), B= (-2,-2) and C = (1,0)

And, assume the medians be AD, BE and CF.

Now, D = [ (-2+1)/2, (-2+0)/2] = ( - 1/2 , -1)

And, E = [ (2+1)/2, (1+0)/2] = (3/2 , 1/2)

And, F = [ ( 2-2)/2, (1-2)/2] = (0 , - 1/2)

AD^2 = (2+1/2)^2 + (1+1)^2 = 41/4 sq. units.

BE^2 = ( 3/2+2)^2 + (2+1/2)^2 = 74/4 sq. units.

CF^2 = (1-0)^2 + (0+1/2)^2 = 5/4 sq. units.

So, AD^2 + BE^2 + CF^2 = 41/4+74/4 +5/4 = 120/4= 30 sq. units. (answer)