Question

the perimeter of the rectangle formed with (2,-2)(8,4)(5,7)(-1,1) as vertices is???

Answer 1

Hii friend,

Here is your answer,

Let, A=(2,-2), B=(8,4), C=(5,7), D=(-1,1)
Now,
To find perimeter of the rectangle first we need to find the side lengths of the rectangle,
Thus, to find the lengths we can use the distance formula,

Therefore,
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

AB = √[(8-2)^2 + (4+2)^2]
AB = √[(6)^2 + (6)^2]
AB = √(36 + 36)
AB = √72 = 6√2 units = 'L'
Similarly,
BC = 3√2 units = 'B'
CD = 6√2 units and
DA = 3√2 units

Therefore,
Perimeter of rectangle = 2(L + B)
Perimeter = 2(6√2 + 3√2)
Perimeter = 2(9√2)
Perimeter = 18√2 units.

Therefore perimeter of the rectangle = 18√2 units.


Hope it helps you.
Thank you.