Square LAMP has vertices L(-2, -3), A(4, -1), M(2,5), and P(-4, 3). What is the perimeter of the square?

The perimeter of the square LAMP is 8 units

Step-by-step explanation:

The rule of the distance between two points (x1, y1) and (x2, y2) is

d =

∵ LAMP is a square

∵ The sides of the square are equal in lengths

∴ LA = AM = MP = PL

Let us find the length of one side of it

∵ L = (-2, -3) and A = (4, -1)

∴ x1 = -2 and y1 = -3

∴ x2 = 4 and y2 = -1

→ Substitute them in the rule of the distance above to find LA

∵ LA =

∴ LA =

∴ LA =

∴ LA = =

→ Simplify the root

∴ LA = 2 units

∵ The perimeter of the square = 4 × side

∴ The perimeter of the square = 4 × 2

∴ The perimeter of the square = 8

∴ The perimeter of the square LAMP is 8 units

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: