Question

distance between two points in the plane: exact answers
try again
your answer is incorrect.
calculate the distance between the points ( f = (-8,1) ) and ( g = (-1,5) ) in the coordinate plane.
give an exact answer (not a decimal approximation).

Explanation:

Step1: Identify the coordinates

Let \( (x_1,y_1)=(-8,1) \) and \( (x_2,y_2)=(-1,5) \)

Step2: Use the distance formula

The distance formula between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \)
Substitute the values:
\( x_2 - x_1=-1-(-8)=-1 + 8=7 \)
\( y_2 - y_1=5 - 1=4 \)
Then \( d=\sqrt{7^2+4^2}=\sqrt{49 + 16}=\sqrt{65} \)

Answer:

\(\sqrt{65}\)