The midpoint of CD¯¯¯¯¯¯¯¯
is E (2, -1). One endpoint is C (-9,4). What are the coordinates of the other endpoint?(1 point)
Responses
(13, -6)
(13, -6)
(7, -2)
(7, -2)
(-3.5, 1.5)
(-3.5, 1.5)
(8, -3)
To find the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (E) is the average of the x-coordinates and the average of the y-coordinates of the two endpoints.
Let's assume the coordinates of the other endpoint are (x, y).
Since the midpoint is (2, -1), we can set up the following equations:
2 = (x + (-9))/2
-1 = (y + 4)/2
Solving these equations, we get:
x + (-9) = 2*2
x - 9 = 4
x = 4 + 9
x = 13
y + 4 = 2*(-1)
y + 4 = -2
y = -2 - 4
y = -6
Therefore, the coordinates of the other endpoint are (13, -6). Thus, the correct answer is:
(13, -6)
To find the coordinates of the other endpoint, we can use the midpoint formula, which states that the coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints.
Let the coordinates of the other endpoint be (x, y).
Using the midpoint formula:
x-coordinate: (x1 + x2) / 2 = (x + (-9)) / 2 = 2
Simplifying, we get: x - 9 = 4
Adding 9 to both sides, we get: x = 13
y-coordinate: (y1 + y2) / 2 = (y + 4) / 2 = -1
Simplifying, we get: y + 4 = -2
Subtracting 4 from both sides, we get: y = -6
Therefore, the coordinates of the other endpoint are (13, -6).
To find the coordinates of the other endpoint, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (E) between two endpoints (C and D) can be found by taking the average of the x-coordinates and the average of the y-coordinates.
Let's denote the coordinates of the other endpoint as (x, y).
The x-coordinate of the midpoint (E) is given as 2, and the x-coordinate of endpoint C is -9. So, we can find the average of these two values:
(x + (-9)) / 2 = 2
(x - 9) / 2 = 2
x - 9 = 4
x = 4 + 9
x = 13
Now, let's find the y-coordinate of the other endpoint:
The y-coordinate of the midpoint (E) is given as -1, and the y-coordinate of endpoint C is 4. So, we can find the average of these two values:
(y + 4) / 2 = -1
y + 4 = -2
y = -2 - 4
y = -6
Therefore, the coordinates of the other endpoint are (13, -6).