Question

the vertices of Triangle are A(-5,-1), B (3,-5),C(5,2).show that the area of the triangle is four times the area of the triangle formed by the joining the midpoint s of the sides??​

Answer 1

Answer: 1 squnit.

Step-by-step explanation: In the figure, ABC is a triangle with vertices  A(2,1), B(4,3) and C(2,5). ΔDEF is formed bu joining the mid-points D, E and F of the sides AB, BC and CA respectively of ΔABC.

Co-ordinates of point D are given by

Co-ordinates of point E are

And, co-ordinates of point F are

Therefore, area of ΔDEF is given as

Thus, the area of the triangles formed by joining the mid-points is