Answer:
The distance between the two points is 5 √ 2
Step-by-step explanation:
Using the distance formula,
⇒
d = √ ( x 1 − x 2 ) ^2 + ( y 1 − y 2 ) ^2
we can plug in our points,
⇒
P 1= ( − 4 , 6 )
⇒
P 2 = ( 3 , 7 )
and solve for the distance:
⇒
d = √ ( x 1 − x 2 ) ^2+ ( y 1 − y 2 ) ^2
⇒ d = √( ( − 4 − 3 )^ 2 + ( 6 − 7 ) ^2)
⇒ d = √ (( − 7 ) ^2 + ( − 1 )^ 2)
⇒ d = √( 49 + 1)
⇒ d = √ 50
⇒ d = √( 25 ⋅ 2)
⇒ d = √( 5^ 2 ⋅ 2)
⇒ d = √ 5 ^2 ⋅ √ 2
⇒ d = 5 ⋅ √ 2
⇒ d = 5 √ 2