Final answer:
The distance between points P and Q is approximately 12.806 units. The midpoint of the line segment connecting P and Q is (-1, 0). The slope of the line passing through P and Q is 5/4. The radius of the circle with center at P passing through Q is approximately 12.806 units.
Step-by-step explanation:
(a) Distance between P and Q:
To find the distance between two points P(-5, -5) and Q(3, 5), we can use the distance formula:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
Substituting the coordinates of P and Q into the formula, we get:
d = sqrt((3-(-5))^2 + (5-(-5))^2)
d = sqrt((8)^2 + (10)^2)
d = sqrt(64 + 100)
d = sqrt(164)
d ≈ 12.806
The distance between P and Q is approximately 12.806 units.
(b) Midpoint of line segment PQ:
To find the midpoint of line segment PQ, we can use the midpoint formula:
M = ((x1+x2)/2, (y1+y2)/2)
Substituting the coordinates of P and Q into the formula, we get:
M = ((-5+3)/2, (-5+5)/2)
M = (-1, 0)
The midpoint of line segment PQ is (-1, 0).
(c) Slope of line passing through P and Q:
To find the slope of the line passing through P and Q, we can use the slope formula:
m = (y2-y1)/(x2-x1)
Substituting the coordinates of P and Q into the formula, we get:
m = (5-(-5))/(3-(-5))
m = 10/8
m = 5/4
The slope of the line passing through P and Q is 5/4.
(d) Radius of the circle with center at P passing through Q:
To find the radius of the circle, we can use the distance formula again:
r = sqrt((x2-x1)^2 + (y2-y1)^2)
Substituting the coordinates of P and Q into the formula, we get:
r = sqrt((3-(-5))^2 + (5-(-5))^2)
r = sqrt((8)^2 + (10)^2)
r = sqrt(64 + 100)
r = sqrt(164)
r ≈ 12.806
The radius of the circle with center at P passing through Q is approximately 12.806 units.