Answer:
The perimeter = 26 unites
Step-by-step explanation:
* Lets revise some facts of parallelogram
- Every two opposite sides are parallel and equal
- Every two opposite angles are equal
- Every two adjacent angles are supplementary
- Th two diagonals bisects each other
- The perimeter = 2(S1 + S2)
* Now lets solve the problem
- ABCD is a parallelogram, where
A = (-2 , 6) , B = (1 , 2) , C = (-2 , -2) , D = (1 , -6)
- To find the perimeter we need the length of AB and BD
- The rule of the distance between two point is
d = √[(x2 - x1)² + (y2 - y1)²]
* Lets find AB
∵ AB = √[1 - -2)² + (2 - 6)²] = √[(3²) + (-4)²]
∴ AB = √25 = 5
* Lets find BD
∵ BD = √[(1 - 1)² + (-6 - 2)² = √[(0)² + (-8)²]
∴ BD = √64 = 8
* Lets find the perimeter
∵ The perimeter = 2 (5 + 8) = 26 unites
