Question

class 10 exercise number 7.3 3rd question answer​

Answer 1

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:

1:4

Explanation:

Let the vertices of the triangle be A (0, -1), B (2, 1), C (0, 3).

Let D, E, F be the mid-points of the sides of this triangle.

Coordinates of D, E, and F are given by

D = ( , ) = (1, 0)

E = ( , ) = (0, 1)

F = ( , ) = (1, 2)

Area of a triangle =

Area of ΔDEF = 1/2 {1(2-1) + 1(1-0) + 0(0-2)} = 1/2 (1+1) = 1

Area of ΔDEF is 1 square units

Area of ΔABC = 1/2 [0(1-3) + 2{3-(-1)} + 0(-1-1)] = 1/2 {8} = 4

Area of ΔABC is 4 square units

Therefore, the required ratio is 1:4.