For the points (6, - 1) and (8, - 9),
(a) Find the exact distance between the points.
(b) Find the midpoint of the line segment whose endpoints are the given points.
(a) To find the distance between the points (6, -1) and (8, -9), we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((8 - 6)^2 + (-9 - (-1))^2)
Distance = √(2^2 + (-8)^2)
Distance = √(4 + 64)
Distance = √68
Therefore, the exact distance between the points is √68.
(b) To find the midpoint of the line segment whose endpoints are the given points, we can use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((6 + 8)/2, (-1 - 9)/2)
Midpoint = (14/2, -10/2)
Midpoint = (7, -5)
Therefore, the midpoint of the line segment whose endpoints are the given points is (7, -5).