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 (x_{1}, y_{1}) and (x_{2}, y_{2}) 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 (x

_{1}, y

_{1}) , (x

_{2}, y

_{2}) and (x

_{3}, y

_{3}) 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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