The midpoint of CD is E(-1,0). One endpoint is C (5, 2). What are the coordinates of the other endpoint?
Let's assume that the other endpoint is D(x,y).
To find the midpoint of CD, we use the following midpoint formula:
Midpoint = ( (x1+x2)/2, (y1+y2)/2 )
Given that the midpoint E = (-1,0), and one endpoint is C = (5,2), we can substitute these values into the formula:
(-1,0) = ( (5+x)/2, (2+y)/2 )
This gives us two equations:
-1 = (5+x)/2 (Equation 1)
0 = (2+y)/2 (Equation 2)
Solving Equation 1 for x:
-1 = (5+x)/2
-2 = 5+x
x = -2-5
x = -7
Solving Equation 2 for y:
0 = (2+y)/2
0 = 2+y
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 formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Given that the midpoint of CD is E(-1,0), and one endpoint is C(5,2), we can substitute the values into the formula and solve for the missing endpoint.
Let the coordinates of the other endpoint be D(x, y).
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
E(-1,0) = ((5 + x)/2, (2 + y)/2)
We can now solve for x and y.
-1 = (5 + x)/2 (solve for x)
Multiply both sides by 2:
-2 = 5 + x
Subtract 5 from both sides:
-2 - 5 = x
x = -7
0 = (2 + y)/2 (solve for y)
Multiply both sides by 2:
0 = 2 + y
Subtract 2 from both sides:
0 - 2 = y
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 the midpoint of a line segment. The midpoint formula states that the coordinates of the midpoint (E) of a line segment with endpoints (C) and (D) can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Given that the midpoint E is (-1, 0) and one endpoint C is (5, 2), we can set up the following equations:
Midpoint x-coordinate = (Endpoint1 x-coordinate + Endpoint2 x-coordinate) / 2
-1 = (5 + Endpoint2 x-coordinate) / 2
Midpoint y-coordinate = (Endpoint1 y-coordinate + Endpoint2 y-coordinate) / 2
0 = (2 + Endpoint2 y-coordinate) / 2
To find the x-coordinate of the other endpoint (D), we can solve for Endpoint2 x-coordinate:
-1 = (5 + Endpoint2 x-coordinate) / 2
Multiply both sides of the equation by 2:
-2 = 5 + Endpoint2 x-coordinate
Rearranging the equation, we get:
Endpoint2 x-coordinate = -2 - 5
Endpoint2 x-coordinate = -7
So, the x-coordinate of the other endpoint D is -7.
To find the y-coordinate of the other endpoint (D), we can solve for Endpoint2 y-coordinate:
0 = (2 + Endpoint2 y-coordinate) / 2
Multiply both sides of the equation by 2:
0 = 2 + Endpoint2 y-coordinate
Subtract 2 from both sides of the equation:
Endpoint2 y-coordinate = -2
So, the y-coordinate of the other endpoint D is -2.
Therefore, the coordinates of the other endpoint D are (-7, -2).