Question

The vertices of a triangle ABC are.........

Answer 1

Answer:

Step-by-step explanation:

Let us mark the mid-points of sides AB, BC and CA as D, E and F respectively. Join DE, EF, and DF to form a ΔDEF.

1) Since D, E and F are the mid points of the ΔABC respectively it will divide all the three sides in the ratio 1:1.

2) Using the section formula: (m1x2 + m2x1/m1 + m2, m1y2 + m2y1/ m1 + m2)

where m1 = 1, m2 = 1; find the points D, E and F.

3) Find the area of ΔABC using the formula: x1 (y2-y3) + x2 (y3-y1) + x3 (y1-y2).

4) Similarly, find the area of ΔDEF.

5) On dividing the area of ΔDEF by the area ΔABC, you will get 4 as the answer.

It implies that area of ΔDEF is 4 times the area of ΔABC.