Question

find the distance between p(4,2) and q(6,6). the distance between p and q is \boxed{}. (simplify your answer. type an exact answer using radicals as needed.)

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify coordinates

For points \( P(4, 2) \) and \( Q(6, 6) \), we have \( x_1 = 4 \), \( y_1 = 2 \), \( x_2 = 6 \), \( y_2 = 6 \).

Step3: Substitute into formula

\( d = \sqrt{(6 - 4)^2 + (6 - 2)^2} = \sqrt{(2)^2 + (4)^2} \)

Step4: Simplify

\( \sqrt{4 + 16} = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5} \)

Answer:

\( 2\sqrt{5} \)