Question

A segment has an endpoint at (5, -2). The midpoint of the segment is (2, 2). What is the length of the segment?

Answer 1

To find the length of the segment, we can use the midpoint and distance formula. First, we find the coordinates of the other endpoint using the midpoint formula. Then, we plug the coordinates into the distance formula to calculate the length of the segment.

Step-by-step explanation:

To find the length of a segment given its midpoint and one endpoint, you can use the midpoint formula. The formula is:

Midpoint = (x1 + x2)/2, (y1 + y2)/2

Let's call the other endpoint (x, y). Plugging in the given information, we get:

(2, 2) = (5 + x)/2, (-2 + y)/2

Simplifying the equation, we have:

2 = (5 + x)/2

4 = 5 + x

x = -1

And

2 = (-2 + y)/2

4 = -2 + y

y = 6

So the other endpoint is (-1, 6). Using the distance formula, we can find the length of the segment:

Distance = sqrt((-1 - 5)^2 + (6 - (-2))^2) = sqrt((-6)^2 + (8)^2) = sqrt(36 + 64) = sqrt(100) = 10