Drag to match each set of points to the correct formula to find \( A B \). \( \begin{array}{ll}\because A(-1,-5) \text { and } B(-8,-2) & \rightarrow \sqrt{(8+1)^{2}+(-2-5)^{2}} \\ \vdots A(-1,5) \text { and } B(8,-2) & \rightarrow \sqrt{(-8-1)^{2}+(-2-5)^{2}} \\ \vdots A(1,5) \text { and } B(-8,-2) & \rightarrow \sqrt{(-8+1)^{2}+(-2+5)^{2}}\end{array} \)

To find the distance \( AB \) between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), we use the distance formula: \[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Now, let's analyze each set of points and match them with the correct formula. 1. **For \( A(-1, -5) \) and \( B(-8, -2) \)**: - Here, \( x_1 = -1 \), \( y_1 = -5 \), \( x_2 = -8 \), and \( y_2 = -2 \). - The distance formula becomes: \[ AB = \sqrt{(-8 - (-1))^2 + (-2 - (-5))^2} = \sqrt{(-8 + 1)^2 + (-2 + 5)^2} = \sqrt{(-7)^2 + (3)^2} = \sqrt{49 + 9} = \sqrt{58} \] - This matches with the formula \( \sqrt{(8+1)^{2}+(-2-5)^{2}} \). 2. **For \( A(-1, 5) \) and \( B(8, -2) \)**: - Here, \( x_1 = -1 \), \( y_1 = 5 \), \( x_2 = 8 \), and \( y_2 = -2 \). - The distance formula becomes: \[ AB = \sqrt{(8 - (-1))^2 + (-2 - 5)^2} = \sqrt{(8 + 1)^2 + (-2 - 5)^2} = \sqrt{(9)^2 + (-7)^2} = \sqrt{81 + 49} = \sqrt{130} \] - This matches with the formula \( \sqrt{(-8-1)^{2}+(-2-5)^{2}} \). 3. **For \( A(1, 5) \) and \( B(-8, -2) \)**: - Here, \( x_1 = 1 \), \( y_1 = 5 \), \( x_2 = -8 \), and \( y_2 = -2 \). - The distance formula becomes: \[ AB = \sqrt{(-8 - 1)^2 + (-2 - 5)^2} = \sqrt{(-9)^2 + (-7)^2} = \sqrt{81 + 49} = \sqrt{130} \] - This matches with the formula \( \sqrt{(-8+1)^{2}+(-2+5)^{2}} \). Now, we can summarize the matches: - \( A(-1, -5) \) and \( B(-8, -2) \) → \( \sqrt{(8+1)^{2}+(-2-5)^{2}} \) - \( A(-1, 5) \) and \( B(8, -2) \) → \( \sqrt{(-8-1)^{2}+(-2-5)^{2}} \) - \( A(1, 5) \) and \( B(-8, -2) \) → \( \sqrt{(-8+1)^{2}+(-2+5)^{2}} \)