Question

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.

Answer 1

Given: A (0, – 1), B (2, 1) and C (0, 3) are the vertices of △ABC. 

Let D, E and F be the midpoints of the sides \(\overline{AB}\), \(\overline{BC}\) and \(\overline{AC}\) .

Area of a triangle ABC =

=\(\frac{1}{2}[8]\)

= 4 sq. units

Area of △DEF =

= 1 sq.units 

Ratio of areas = △ABC : △DEF = 4 : 1. 

△ADF ≅ △BED ≅ ≅ △CE△DEFF 

∴ △ABC : △DEF = 4 : 1