show me how to solve this problem:
Given an endpoint, C, and a midpoint, M, find the other endpoint, D, when
C= (3,3), M= (0,0)
look at the distance from M to C, then reverse it to get D
from Mx to Cx it is -3, so the reverse would be +3, or Dx is -3
D=(-3,-3)
To find the other endpoint, D, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, M, between two endpoints, C and D, can be found by taking the average of the x-coordinates and the average of the y-coordinates:
Midpoint formula:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that C = (3,3) is one endpoint and M = (0,0) is the midpoint, we can substitute these values into the midpoint formula and solve for the coordinates of the other endpoint, D.
Let's calculate the coordinates of D step by step:
1. Substitute the given values into the midpoint formula:
(0,0) = ((3 + x2) / 2, (3 + y2) / 2)
2. Simplify the equation:
0 = (3 + x2) / 2 --> Multiply both sides by 2 to remove the fraction
0 = 3 + x2 --> Subtract 3 from both sides
-3 = x2
0 = (3 + y2) / 2 --> Multiply both sides by 2 to remove the fraction
0 = 3 + y2 --> Subtract 3 from both sides
-3 = y2
So, we have found that the coordinates of the other endpoint, D, are (-3, -3).
Therefore, the solution to the problem is D = (-3, -3).