Question
The points A and B have coordinates \( (6,1) \) and \( (-2,7) \) respectively. Find the length of AB . (2 marks) \( A B=\square \)
Ask by Simmons Reid. in Singapore
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The length of AB is 10.
Solution
To find the length of segment \( AB \) with points \( A(6, 1) \) and \( B(-2, 7) \), use the distance formula:
\[
AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substitute the coordinates:
\[
AB = \sqrt{(-2 - 6)^2 + (7 - 1)^2} = \sqrt{(-8)^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10
\]
\[
AB = 10
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the length of the line segment \( AB \) between points \( A(6, 1) \) and \( B(-2, 7) \), we can use the distance formula: \[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates: \[ AB = \sqrt{((-2) - 6)^2 + (7 - 1)^2} = \sqrt{(-8)^2 + (6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \] Thus, the length of \( AB \) is \( 10 \). AB = 10
