Question

Show that the points (- 4, - 7),( - 1, 2), (8, 5 )and (5 - 4) taken in order are the vertex of a rhombus .Find its area. ( Hint: Area of rhombus is =1\2 into product of its diagonals)​

Answer 1

Step-by-step explanation:

vector corresponding to each side

A = 3 i + 5 j

B = 9 i + 3 j

C = -3i - 9 j

D = 9i + 3 j

B||C it proves that. it is rhombus

Diagonal vectors are

12 i + 12 j , 6i - 6j

so area = 1/2 × 12 × 6 × ( i + j ) × ( i - j) = 36×2 = 72units