Question

Find the distance d left parenthesis Upper A comma Upper B right parenthesis between points A and B.
Upper A left parenthesis 6 comma negative 2 right parenthesis​; Upper B left parenthesis 6 comma 6 right parenthesis
Question content area bottom
Part 1
d left parenthesis Upper A comma Upper B right parenthesisequals
  
enter your response here ​(Simplify your answer. Type an exact​ answer, using radicals as​ needed.)

Answer 1

To find the distance \( d(A, B) \) between the points \( A(6, -2) \) and \( B(6, 6) \), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \( A \) has coordinates \( (x_1, y_1) = (6, -2) \) and \( B \) has coordinates \( (x_2, y_2) = (6, 6) \).

Substituting the coordinates into the formula, we have:

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

Calculating the differences:

\[
d = \sqrt{(0)^2 + (6 + 2)^2}
\]
\[
= \sqrt{0 + 8^2}
\]
\[
= \sqrt{64}
\]
\[
= 8
\]

Thus, the distance \( d(A, B) \) is

\[
d(A, B) = 8.
\]

So, you can enter:

\( d(A, B) = 8 \).