The point D is (7, 8) for which the given coordinates of A(3, 6), B(5, 2), and C(9, 4), make a square.
What is a square?
It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.
Line AB and CD are parallel to each other.
Line AB:
(y- 6) = -2(x-3)
y - 6 = -2x+6
2x+y = 12
Line CD:
2x + y = d
Plug (9,4)
18+4 = d
d = 22
2x + y = 22 ...(1)
Line BC:
(y - 2) = 1/2(x-5)
2y -4 = x-5
-x + 2y = -1
x - 2y = 1
Line AD:
x - 2y = e
3 - 12 = e
e = -9
x-2y = -9 ...(2)
The intersection point of (1) and (2)
x = 7 and y = 8
Thus, the point D is (7, 8) for which the given coordinates of A(3, 6), B(5, 2), and C(9, 4), make a square.
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