When a fair die is rolled, find the probability of rolling the following:

2 or 6

Hey there!!

Basic formula :

√( x₂ - x₁ )² + (y₂ - y₁ )²

Coordinates :

R ( -1 , 3 ) ; S ( 3 , 3 ) ; T ( 5 , -1 ) ; U ( -2 , -1 )

Let us see the distance of the segment of RS

( x₂ = 3 , x₁ = -1 )  ( y₂ = 3 , x₁ = 3 )

√ ( 3 - ( -1 ) )² + ( 3 - 3 )²

√ ( 3 + 1 )² + ( 0 )²

√ ( 4 )² + 0

√ 16

= 4

First side = 4

Now, let us find the ST

( 3 , 3 ) ( 5 , - 1 )

( x₂ = 5 , x₁ = 3 ) ; ( y₂ = -1 , y₁ = 3 )

√ ( 5 - 3 )² + ( -1 - 3 )²

√ ( 2 )² + ( -4 )²

√ 4 + 16

√20

√4 × √5

the length of this side = 2√5 = 4.47

The length of TU :

( 5 , -1 ) ( -2 , -1 )

( x₂ = -2 , x₁ = 5 ) ; ( y₂ = -1 , y₁ = -1 )

√ ( -2 -5 )² + ( -1 + 1 )²

√ ( -7 )² + ( 0 )²

√ 49 = 7

The length of the third side = 7

The length of RU :

( -1 , 3 ) ( -2 , -1 )

( x₂ = -2  , x₁ = -1 ) ; ( y₂ = -1 , y₁ = 3 )

√ ( -2 + 1 )² + ( -1-4 )²

√ ( - 1 )² + ( -5 )²

√ 1 + 25

√26 = 5.09

The length of the fourth side = 5.09

Perimeter = 4 + 4.47 + 7 + 5.09

= 20.56

The perimeter = 20.56

Rounded off = 21 0r 20.6

Hope my answer helps!