Question

For the points (-3,-1) and (-5,9),

(a) Find the exact distance between the points.
(b) Find the midpoint of the line segment whose endpoints are the given points.

Answer 1

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).