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

Let A (0, –1), B (2, 1) and C (0, 3) are the vertices of the triangle.

D, E and F are the mid–points of the sides AB, BC and AC respectively.

Mid – point formula =

Mid – point of AB

D = (1,0)

Mid – point of BC =

Mid – point of AC =

Area of Δ ABC:

Area of triangle =

x₁ = 0, x₂ = 2 and x₃ = 0

y₁ = –1, y₂ = 1 and y₃ = 3

⇒

⇒

⇒

⇒

⇒ 4 sq. units

Area of Δ DEF:

Area of triangle =

x₁ = 1, x₂ = 1 and x₃ = 0

y₁ = 0, y₂ = 2 and y₃ = 1

⇒

⇒

⇒

⇒

⇒ 1 sq. units

Area of triangle ABC: Area of triangle DEF

4: 1