the midpoint of CD is E (-1,0). one endpoint is C (5,2). what are the coordinates of the other endpoint
Let the other endpoint be (a,b)
so ...
(a+5)/2 = -1 and (b+2)/2 = 0
a+5 = -2 and b+2 = 0
a = -7, b = -2
then the other endpoint is (-7,-2)
Well, if E is the midpoint of CD, and E is located at (-1,0), that means CD is divided into two equal halves. So, to find the coordinates of the other endpoint, we can use the formula for finding the midpoint, which is [(x₁ + x₂)/2, (y₁ + y₂)/2].
Since we know E is (-1,0) and C is (5,2), we can substitute these values into the formula:
[(-1 + x₂)/2, (0 + y₂)/2] = (5,2)
Now, let's simplify this equation:
(-1 + x₂)/2 = 5
=> -1 + x₂ = 10
=> x₂ = 11
(0 + y₂)/2 = 2
=> 0 + y₂ = 4
=> y₂ = 4
Therefore, the coordinates of the other endpoint are (11, 4). Voila!
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 equal to the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Therefore, we can set up the following equations using the coordinates given:
x-coordinate of E = (x-coordinate of C + x-coordinate of D) / 2
-1 = (5 + x-coordinate of D) / 2
Simplifying the first equation, we get:
-2 = 5 + x-coordinate of D
Subtracting 5 from both sides, we get:
x-coordinate of D = -7
Now, let's solve for the y-coordinate of D using the y-coordinate of E and the y-coordinate of C:
y-coordinate of E = (y-coordinate of C + y-coordinate of D) / 2
0 = (2 + y-coordinate of D) / 2
Simplifying the equation, we get:
0 = 2 + y-coordinate of D
Subtracting 2 from both sides, we get:
y-coordinate of D = -2
Therefore, the coordinates of the other endpoint, D, are (-7, -2).
To find the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints.
Let's say the coordinates of the other endpoint are (x, y). We know that the midpoint of CD is E(-1, 0) and one endpoint is C(5, 2).
Using the midpoint formula, we can calculate the x-coordinate of the other endpoint:
x-coordinate = (x-coordinate of C + x-coordinate of E) / 2
Substituting the known values:
(-1) = (5 + x) / 2
Now we can solve for x:
-2 = 5 + x
x = -7
Next, we can calculate the y-coordinate of the other endpoint:
y-coordinate = (y-coordinate of C + y-coordinate of E) / 2
Substituting the known values:
0 = (2 + y) / 2
Solving for y:
0 = 2 + y
y = -2
Therefore, the coordinates of the other endpoint are (-7, -2).