Final answer:
The distance between P(-7, 25) and Q(-2, 30) is approximately 7.07 units. The coordinates of the midpoint of the segment PQ are (-9/2, 55/2).
Step-by-step explanation:
The distance between two points in the Cartesian plane can be found using the distance formula:
d(P,Q) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the points. Plugging in the values for P(-7,25) and Q(-2,30), we get:
d(P,Q) = sqrt((-2 - (-7))^2 + (30 - 25)^2)
d(P,Q) = sqrt(5^2 + 5^2)
d(P,Q) = sqrt(50)
d(P,Q) ≈ 7.07
The midpoint of the segment PQ can be found using the midpoint formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
Plugging in the values for P(-7,25) and Q(-2,30), we get:
M = ((-7 + (-2))/2, (25 + 30)/2)
M = (-9/2, 55/2)
So the distance between P and Q is approximately 7.07 and the coordinates of the midpoint M are (-9/2, 55/2).
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