Question

Find the perimeter of parallelogram ABCD with vertices A(–2, 6), B(1, 2), C(–2, –2), and D(1, –6).

Answer 1

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

Answer 2

Answer:

26 units

Step-by-step explanation:

The attached image shows the coordinates drawn as a parallelogram.

The perimeter is sum of all the sides, AB + BD + DC + CA

Both BD and CA are straight lines with 8 units

AB and DC are not straight lines. So we need to find it using the pythagorean theorem, which is , one leg squared of a triangle + another leg squared will give us hypotenuse squared.

Looking at the triangle AYB, we can write and solve for AB:

$AY^2+YB^2=AB^2\\4^2 + 3^2 = AB^2\\16+9=AB^2\\25=AB^2\\AB=5$

we can use the same argument and lengths for the triangle CXD. We will have DC = 5 units

Perimeter = AB + BD + DC + CA = 5 + 8 + 5 + 8 = 26 units