Final answer:
The exact distance between the points (-1, -8) and (6, -9) is 5sqrt(2) units. The midpoint of the line segment with endpoints (-1, -8) and (6, -9) is (5/2, -17/2).
Step-by-step explanation:
To find the exact distance between two points, we can use the distance formula. Let's label the coordinates of point 1 as (x1, y1) and point 2 as (x2, y2). The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the two points are (-1, -8) and (6, -9). Plugging these values into the distance formula, we get:
d = sqrt((6 - (-1))^2 + (-9 - (-8))^2)
= sqrt((7)^2 + (-1)^2)
= sqrt(49 + 1)
= sqrt(50)
= 5sqrt(2)
So, the exact distance between the points (-1, -8) and (6, -9) is 5sqrt(2) units.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found by taking the average of the x-coordinates and the average of the y-coordinates. Let's label the coordinates of point 1 as (x1, y1) and point 2 as (x2, y2). The midpoint formula is:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the coordinates of the two points are (-1, -8) and (6, -9). Plugging these values into the midpoint formula, we get:
(x, y) = ((-1 + 6)/2, (-8 + (-9))/2)
= (5/2, -17/2)
So, the midpoint of the line segment with endpoints (-1, -8) and (6, -9) is (5/2, -17/2).