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Hello, the solution is MUCH SIMPLER (!).
From the point D(1,6) to the center C(4,1), you move 3 units horizontally in positive direction of x-axis;
hence, to get the other diameter's endpoint, you CONTINUE to move another 3 units horizontally along x-axis
from coordinate x= 4 (center) to x= 4+3 = 7 (endpoint).
Similarly,
from the point D(1,6) to the center C(4,1), you move 5 units vertically in negative direction of y-axis;
hence, to get the other diameter's endpoint, you CONTINUE to move another 5 units vertically along y-axis
from coordinate y= 1 (center) to y= 1-5 = -4 (endpoint).
Thus, the other midpoint coordinates are x= 7, y =-4, and the endpoint itself is (7,-4). ANSWER
That is all.
YOU DO NOT NEED solve any complicated equations to solve this SUPER-simple problem (!)
You do not need write this Master's thesis that another tutor impose you (!)
May the LORD saves you of doing this UNNECESSARY work (!)
M E M O R I Z E this algorithm as a mantra and use it EVERY TIME when you solve similar problems (!)
On a test, normal time to complete such assignment is 10 - 15 seconds.