11. The midpoint of is E(–1, 0). One endpoint is C(5, 2). What are the coordinates of the other endpoint?
can someone please explain how to do this problem
For the x-coordinate,
C is 6 units to the right of E
For the y-coordinate,
C is 2 units above E
So, since E is the midpoint, the other endpoint is
6 to the left and 2 below E, or (-7,-2)
Algebraically, you know that if the ends are C and D,
(Cx+Dx)/2 = Ex
(Cy+Dy)/2 = Ey, so
(5+Dx)/2 = -1
(2+Dy)/2 = 0
5+Dx = -2
Dx = -7
2+Dy = 0
Dy = -2
as shown above
thank you
did you use the midpoint formula
To find the coordinates of the other endpoint, we first need to understand the concept of a midpoint.
The midpoint of a line segment is the point that is equidistant from both endpoints. It lies exactly halfway between the two endpoints of the line segment. Mathematically, the midpoint can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Let's break down the problem step by step:
1. Given that the midpoint is E(-1, 0) and one endpoint is C(5, 2), we can use the midpoint formula to find the other endpoint. The midpoint formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
2. Plug in the coordinates of the midpoint and one endpoint:
Midpoint = ((-1 + x2)/2, (0 + y2)/2)
Endpoint = (5, 2)
3. Solve for the other endpoint:
(-1 + x2)/2 = 5 --> x2 - 1 = 10 --> x2 = 11
(0 + y2)/2 = 2 --> y2/2 = 2 --> y2 = 4
4. Therefore, the coordinates of the other endpoint are (11, 4).
So, the other endpoint of the line segment is (11, 4).