Find the distance between the points \((-3, -3)\) and \((6, 12)\). Round the answer to the nearest hundredth, if necessary.
Answer (3)
A = ( x A ; y A ) an d B = ( x B ; y B ) ⇒ ∣ A B ∣ = ( x A − x B ) 2 + ( y A − y B ) 2 − − − − − − − − − − − − − − − − − − − − − − A = ( − 3 ; − 3 ) ; B = ( 6 ; 12 ) ∣ A B ∣ = ( − 3 − 6 ) 2 + ( − 3 − 12 ) 2 = . = 81 + 225 = 306 = 3 34 ≈ 17.49
( − 3 , − 3 ) , ( 6 , 12 ) d i s t an ce f or m u l a : d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d = ( 6 − ( − 3 ) ) 2 + ( 12 − ( − 3 ) ) 2 = ( 6 + 3 ) 2 + ( 12 + 3 ) 2 = 9 2 + 1 5 2 = = 81 + 225 = 306 = 9 ⋅ 34 = 3 34 = 3 ⋅ 5.83 = 17.49
The distance between the points ( − 3 , − 3 ) and ( 6 , 12 ) is approximately 17.49 when rounded to the nearest hundredth. This result was calculated using the distance formula. The formula involves finding the differences between the coordinates, squaring those differences, summing them, and then taking the square root.
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