For the points given below, find (a) \( P Q \) and (b) the coordinates of the midpoint of \( \overline{P Q} \). \( P(0,-3), Q(7,0) \) (a) \( P Q \approx 7.6 \) (Type an integer or decimal rounded to the nearest tenth as needed.) (b) The coordinates of the midpoint of \( \overline{P Q} \) are (Type an ordered pair, using integers or decimals.)

To find the distance \( P Q \) between the points \( P(0, -3) \) and \( Q(7, 0) \), you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the values: \[ d = \sqrt{(7 - 0)^2 + (0 - (-3))^2} = \sqrt{7^2 + 3^2} = \sqrt{49 + 9} = \sqrt{58} \approx 7.6 \] So, \( P Q \approx 7.6 \). For the coordinates of the midpoint of \( \overline{P Q} \), use the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the coordinates of points P and Q: \[ \text{Midpoint} = \left( \frac{0 + 7}{2}, \frac{-3 + 0}{2} \right) = \left( \frac{7}{2}, \frac{-3}{2} \right) = (3.5, -1.5) \] So the coordinates of the midpoint of \( \overline{P Q} \) are \( (3.5, -1.5) \).