I am looking everywhere.....in my notes and in my chapter. What would the other endpoint of a line segment with the given midpoint and one endpoint?

ENDPOINT (0,0) MIDPOINT (2, -8)

Use the midpoint formula:

x coordinate: (1st_x + 1st_y)/2
y coordinate: (2nd_x + 2nd_y)/2

So you could put it into an equation like this:

2 = (0 + x)/2 (for the x coordinate)

-8 = (0+ y)/2 (for the y coordinate)

I know it may have seemed confusing how I wrote it out, so please ask if you need any clarification of my solution.

let the other endpoint be (a,b)

using the midpoint formula
((a+0)/2,(b+0)/2) = (2,-8)
so a/2 = 2 or a=4
and b/2 = -8, or b = -16

the other endpoint is (4,-16)

check by finding the midpoint between (0,0) and (4,-16)

thank you both!!!

To find the other endpoint of a line segment given a midpoint and one endpoint, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint `(x, y)` can be found by taking the average of the coordinates of the two endpoints `(x1, y1)` and `(x2, y2)`:

x = (x1 + x2) / 2
y = (y1 + y2) / 2

In this case, you have the midpoint as (2, -8) and one endpoint as (0, 0).

Let's call the other endpoint (x2, y2).

Using the midpoint formula, we can set up the equations:

x = (0 + x2) / 2
y = (0 + y2) / 2

We can now solve these equations to find the values of x2 and y2.

From the first equation:
2x = 0 + x2
2x - x2 = 0
x2 = 2x

From the second equation:
-8 = 0 + y2
y2 = -8

Therefore, the other endpoint of the line segment is (2x, -8).

Note: It is important to remember that without more information, there are infinitely many line segments that can have the given midpoint and one endpoint.