The midpoint of line CD is E(-1, 0). One endpoint is C(5, 2). What are the coordinates of the other endpoint?
To find the coordinates of the other endpoint, we need to use the midpoint formula:
Midpoint formula:
M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that the midpoint is E(-1, 0) and one endpoint is C(5, 2), we can express the coordinates of the other endpoint as D(x2, y2) and C(5, 2) respectively.
Using the midpoint formula:
x2 = 2 * x_midpoint - x1
= 2 * (-1) - 5
= -2 - 5
= -7
y2 = 2 * y_midpoint - y1
= 2 * 0 - 2
= 0 - 2
= -2
Therefore, the coordinates of the other endpoint are D(-7, -2).
Let's assume the coordinates of the other endpoint, D, are (x, y).
Since the midpoint of the line CD is E(-1, 0), we can use the midpoint formula to find E:
E = ( (x1 + x2)/2, (y1 + y2)/2 )
where (x1, y1) and (x2, y2) are the coordinates of C and D, respectively.
Substituting the known values into the formula, we have:
-1 = ( (5 + x)/2 )
0 = ( (2 + y)/2 )
Simplifying these equations, we get:
-2 = (5 + x)
0 = (2 + y)
Solving for x and y, we have:
x = -7
y = -2
Therefore, the coordinates of the other endpoint, D, are (-7, -2).
To find the coordinates of the other endpoint, we can use the formula for finding the midpoint of a line segment. The midpoint coordinates (x, y) can be found by taking the average of the x-coordinates and the average of the y-coordinates of the two endpoints.
Given that the midpoint of line CD is E(-1, 0), and one endpoint is C(5, 2), we can find the other endpoint using the following steps:
1. Let's represent the coordinates of the other endpoint as (x2, y2).
2. Calculate the average of the x-coordinates: (x1 + x2) / 2 = (-1 + x2) / 2 = 5 / 2.
Simplifying, we get: -1 + x2 = 5, then x2 = 5 + 1 = 6.
So, the x-coordinate of the other endpoint is 6.
3. Calculate the average of the y-coordinates: (y1 + y2) / 2 = (0 + y2) / 2 = 2 / 2 = 1.
So, the y-coordinate of the other endpoint is 1.
Therefore, the coordinates of the other endpoint are (6, 1).
What is the midpoint formula?
The midpoint formula is a formula used to find the coordinates of the midpoint of a line segment given the coordinates of its two endpoints.
The formula is:
Midpoint(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint.