Find the distance between the pair of points \( (-2,-7) \) and \( (2,-6) \). If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is \( \sqrt{2^{2}} \) units. (Simplify your answer. Type an exact answer, using radicals as needed.)

To find the distance between the points \( (-2, -7) \) and \( (2, -6) \), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where \( (x_1, y_1) = (-2, -7) \) and \( (x_2, y_2) = (2, -6) \). Now, let's substitute the coordinates into the formula: 1. Calculate \( x_2 - x_1 \): \[ x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \] 2. Calculate \( y_2 - y_1 \): \[ y_2 - y_1 = -6 - (-7) = -6 + 7 = 1 \] 3. Now substitute these values into the distance formula: \[ d = \sqrt{(4)^2 + (1)^2} \] 4. Calculate \( (4)^2 \) and \( (1)^2 \): \[ (4)^2 = 16 \quad \text{and} \quad (1)^2 = 1 \] 5. Add these results: \[ d = \sqrt{16 + 1} = \sqrt{17} \] Thus, the exact distance between the points is \( \sqrt{17} \) units. Now, let's round \( \sqrt{17} \) to two decimal places. Calculating \( \sqrt{17} \): \[ \sqrt{17} \approx 4.1231 \] Rounding to two decimal places gives us: \[ \sqrt{17} \approx 4.12 \] In summary, the distance between the points \( (-2, -7) \) and \( (2, -6) \) is \( \sqrt{17} \) units, which is approximately \( 4.12 \) when rounded to two decimal places.