Answer:
d(P, Q) = 7.071067812
M = (-4.5, 5.5)
Explanation:
Finding the distance d(P, Q):
We can find the distance between two points using the distance formula, which is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2], where
- (x1, y1) is one point,
- and (x2, y2) is another point.
Thus, we can find d, the distance, of P and Q by plugging in P(-7, 3) for (x1, y1) and Q(-2, 8) for (x2, y2):
d = √[(-2 - (-7))^2 + (8 -3)^2]
d = √[(-2 + 7)^2 + (5)^2]
d = √[(-5)^2 + 25]
d = √[25 + 25]
d = √[50]
d = 7.071067812
Thus, the distance, d, between P and Q is 7.071067812 units.
If you prefer to simply use √(50) units for the distance, you can do so since its the same as 7.071067812.
Finding the midpoint:
We can find the midpoint between two points using the midpoint formula, which is given by:
M = (x1 + x2) / 2, (y1 + y2) / 2
Thus, we can find M, the midpoint of the segment PQ by plugging in P(-7, 3) for (x1, y1) and Q(-2, 8) for (x2, y2) in the midpoint formula:
M = (-7 + -2) / 2, (3 + 8) / 2
M = (-9) / 2, (11) / 2
M = (-4.5, 5.5)
Therefore, the coordinates of the midpoint of the segment PQ are (-4.5, 5.5)