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.