Question

HELP!!!! NUMBER 2

2. Find the distance between these two points.
First Point
Second Point
Distance
(5, - 2)
(8,6)
(5,6)
(-3,6)
(-3,6)
(5,-2)

Answer 1

Answer:

1. 8

2 . 11

$3 . \sqrt{128} \ or \ 8 \sqrt2$

Step-by-step explanation:

$Distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2 }$

1 . ( 5 , - 2 ) and ( 5 , 6 )

  $Distance = \sqrt{(5 -5)^2 + ( 6-(-2))^2} = \sqrt{ 0 + 8^2 } = \sqrt{64} = 8$

2 . ( 8 , 6 ) and ( - 3 , 6 )

  $Distance = \sqrt{( -3 -8)^2 + ( 6 - 6)^2 } = \sqrt{ (-11)^2 + 0 } = \sqrt { 121 } = 11$

3. ( 5 , - 2 ) and ( -3 , 6 )

  $Distance = \sqrt{(-3 - 5)^2 + ( 6 --2)^2} = \sqrt{(-8)^2 + ( 8)^2} = \sqrt{ 64 + 64 } = \sqrt{128}$

   

          $[ \ \sqrt{128} = \sqrt{ 2 \times 64} = \sqrt{ 2 \times 8^2 } = 8 \sqrt{2} \ ]$