The coordinates of point C are calculated using the midpoint formula since D is the midpoint between C and E. By substituting the given coordinates and solving the equations, we find that the coordinates of point C are (19, 22).
Step-by-step explanation:
The question asks for the coordinates of point C in a coordinate system where CDE is a straight line, CD equals DE, and the coordinates of D and E are known. To find the coordinates of C, we consider the midpoint formula and the fact that D is the midpoint between C and E since CD = DE. We can denote point C's coordinates as (x, y).
Given that point D is the midpoint, the coordinates of D are the averages of the coordinates of points C and E. Therefore, we have:
x-coordinate of D = (x-coordinate of C + x-coordinate of E) / 2
y-coordinate of D = (y-coordinate of C + y-coordinate of E) / 2
Substituting the known values gives us:
13 = (x + 7) / 2
25 = (y + 28) / 2
Solving these equations gives us the coordinates of C as follows:
x = 2 * 13 - 7
y = 2 * 25 - 28
Thus, the coordinates of point C are (19, 22).