For the points given below, find (a) \( P Q \) and (b) the coordinates of the midpoint of \( \overline{\mathrm{PQ}} \). \( P(0,-3), Q(7,2) \) (a) \( P Q \approx \square \) (Type an integer or decimal rounded to the nearest tenth as needed.) (b) The coordinates of the midpoint of \( \overline{\mathrm{PQ}} \) are \( \square \). (Type an ordered pair, using integers or decimals.)

To find the distance \( PQ \) between points \( P(0, -3) \) and \( Q(7, 2) \), we use the distance formula: \[ PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the coordinates, we have: \[ PQ = \sqrt{(7 - 0)^2 + (2 - (-3))^2} = \sqrt{(7)^2 + (5)^2} = \sqrt{49 + 25} = \sqrt{74} \approx 8.6 \] For the midpoint of \( \overline{PQ} \), we use the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Calculating this gives: \[ \text{Midpoint} = \left( \frac{0 + 7}{2}, \frac{-3 + 2}{2} \right) = \left( \frac{7}{2}, \frac{-1}{2} \right) = \left( 3.5, -0.5 \right) \] So, the answers are: (a) \( PQ \approx 8.6 \) (b) The coordinates of the midpoint of \( \overline{PQ} \) are \( (3.5, -0.5) \).