Final answer:
The exact distance between the points (-3,-1) and (-5,9) is 2sqrt(26) m. The midpoint of the line segment between the points is (-4, 4).
Step-by-step explanation:
(a) Exact Distance:
To find the distance between the points (-3,-1) and (-5,9), we can use the distance formula. The formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plug in the coordinates:
d = sqrt((-5 - (-3))^2 + (9 - (-1))^2)
d = sqrt((-5 + 3)^2 + (9 + 1)^2)
d = sqrt((-2)^2 + (10)^2)
d = sqrt(4 + 100)
d = sqrt(104)
d = 2sqrt(26) m
(b) Midpoint:
To find the midpoint of the line segment between the points, we can use the midpoint formula. The formula is:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
Plug in the coordinates:
(x, y) = ((-3 + -5)/2, (-1 + 9)/2)
(x, y) = (-8/2, 8/2)
(x, y) = (-4, 4)
Therefore, the midpoint is (-4, 4).