Q6 of 184 Page 10

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

Let ABC is a triangle with points (0, -1), (2, 1), (0, 3)


To Find: Ratio of area of triangle ABC to triangle DEF


We know that



Area of triangle


Then,


Area of triangle ABC



= 4


Now we have to find point D, E, and F.


Hence D is the midpoint of side BC then,


Coordinates of D



= (1, 2 )


Hence E is the midpoint of side AC then,


Coordinates of E



= (0, 1)


Hence F is the midpoint of side AB then,


Coordinates of F



= (1, 0)


Area of triangle


Now Area of triangle DEF




= 1


Therefore Area of ABC= 4 Area of DEF.


Then, The ratio of ∆DEF and ∆ABC = 1:4


More from this chapter

All 184 →
5

If A, B, C are the points (-1, 5), (3, 1), (5, 7) respectively and D, E, F are the middle points of BC, CA and AB respectively, prove that ΔABC = 4ΔDEF.

 6

Three vertices of a triangle are A(1, 2), B(-3, 6) and C(5, 4). If D, E, and C, respectively, show that the area of triangle ABC is four times the area of triangle DEF.

 7

Find the area of a triangle ABC if the coordinates of the middle points of the sides of the triangle are (-1, - 2), (6, 1) and (3, 5).

 8

The vertices of ΔABC are A(3, 0), B(0, 6) and (6, 9). A straight line DE divides AB and AC in the ratio 1:2 at D and E respectively, prove that