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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