Final answer:
The midpoint of the segment between points P(0,−7) and Q(12,2) is (6, −2.5). The distance between P and Q is 15.0 units, and each point is 7.5 units away from the midpoint.
Step-by-step explanation:
To find the midpoint of the segment with endpoints P(0,−7) and Q(12,2), we use the midpoint formula, which is ( (x_1 + x_2)/2, (y_1 + y_2)/2 ). Applying this formula, we find the midpoint M to be ( (0 + 12)/2, (−7 + 2)/2 ) = (6, −2.5). To find the distance between the points P and Q, we use the distance formula: √((x_2 - x_1)^2 + (y_2 - y_1)^2). Plugging in the coordinates for P and Q, we get the distance D as √((12 - 0)^2 + (2 - (−7))^2) = √(144 + 81) = √225 = 15.0 units. The distance from P to the midpoint M and from Q to the midpoint M will be half of the distance between P and Q, so this would be 15.0 / 2 = 7.5 units.