Q. 34.3( 231 Votes )

Find the area of

Answer :

Let the vertices of the triangle be A (0, - 1), B (2, 1), C (0, 3)
We know, mid-points of a line joining points (x1, y1) and (x2, y2) is given by 

Let D, E, F be the mid-points of the sides of this triangle. Coordinates of D, E, and F are given by


D = (, ) = (1, 0)


E = () = (0, 1)


F = () = (1, 2)


Also, we know area of a triangle having (x1, y1) , (x2, y2) and (x3, y3) is

Area of the triangle (DEF) = [1 (2 – 1) + 1(1- 0) + 0 (0- 2)

= (1 + 1)

= 1 square unit

Area of the triangle (ABC) = = [0 (1 – 3) + 2(3 + 1) + 0 (-1 - 1)

= × 8

= 4 square units

Therefore, required ratio = 1 : 4

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