Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Coordinates of mid-points of AB = P((x₁+x₂)/2), (y₁+y₂)/2) = P((0=2)/2), (-1+1)/2) = P(1,0)
Coordinates of mid-points of BC = R((2+0)/2, (1+3)/2) = R(1,2)
Coordinates of mid-points of AC = Q((0+0)/2, (-1+3)/2) = Q(0,1)
= 1/2[1(2-1)+1(1-0)+0(0-1)] = 1/2[2] = 1 square units
Area of triangle ABC
= 1/2[0(1-3)+2{3-(-1)}+0(-1-1)] = 1/2[8] = 4 square units
Hence, (Area of triangle PQR)/(Area of triangle ABC) = 1/4

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