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Points A and B have symmetry with respect to point C.

Find the coordinates of C given the points:
a) A(3, 4) and B(5, 1) c) A(5, 3) and B(2, 1)
b) A(0, 2) and B(0, 6) d) A(2a, 0) and B(0, 2b)

4 answers

a. A(3,4), C(x,y), B(5,1).
Points A and B are equidistance from C:
x-3 = 5-x
X = 4

y-4 = 1-y
Y = 2 1/2

b. A(0,2), C(x,y), B(0,6).
x-0 = 0-x
X = 0

y-2 = 6-y
Y = 4

c. Same procedure as a, and b.

d. A(2a,0), C(x,y), B(0,2b).
x-2a = 0-x
2x = 2a
X = a

y-0 = 2b-y
2y = 2b
Y = b
Another Method:
a. X = (3+5)/2 = 4
Y = (4+1)/2 = 2.5
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