Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertice are A(5,6),B(1,-2) and C(3,-2).
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If ABCD is a parallelogram,
Then A+C = B+D
D = (x,y)
A+C = (5,6) +(3,-2) = (8,4)
B+D = (1,-2) + (x,y) = (1+x,y-2)
So, 1+x = 8 ⇒ x = 7
y-2 = 4 ⇒ y = 6
So, D (7,6)
Then A+C = B+D
D = (x,y)
A+C = (5,6) +(3,-2) = (8,4)
B+D = (1,-2) + (x,y) = (1+x,y-2)
So, 1+x = 8 ⇒ x = 7
y-2 = 4 ⇒ y = 6
So, D (7,6)
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