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Question

Part 1
Find the distance d left parenthesis Upper A comma Upper B right parenthesisd(A,B) between points A and B.
Upper A left parenthesis 2 comma negative 6 right parenthesisA(2,−6)​; Upper B left parenthesis 2 comma 3 right parenthesisB(2,3)
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Part 1
d left parenthesis Upper A comma Upper B right parenthesisd(A,B)equals=enter your response here ​(Simplify your answer. T

Answer 1

To find the distance \( d(A, B) \) between the points \( A(2, -6) \) and \( B(2, 3) \), we can use the distance formula:

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

Here, the coordinates of point \( A \) are \( (x_1, y_1) = (2, -6) \) and the coordinates of point \( B \) are \( (x_2, y_2) = (2, 3) \).

Substituting the coordinates into the formula:

\[ d(A, B) = \sqrt{(2 - 2)^2 + (3 - (-6))^2} \]

Calculating the differences:

\[ d(A, B) = \sqrt{(0)^2 + (3 + 6)^2} \] \[ d(A, B) = \sqrt{0 + 9^2} \] \[ d(A, B) = \sqrt{81} \] \[ d(A, B) = 9 \]

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

\[ \boxed{9} \]