Question

HW Due Date: Sep 25

Given two adjacent vertices, (x1, y1) and (x2, y2), for a square, find the other two vertices. (Derive formulas for the coordinates of those vertices, in terms of x1, x2, y1 and y2.

Answer 1

Given: (x1, y1) and (x2, y2)

Let's consider a square having adjacent vertices (x1, y1) and (x2, y2)

From the above square, we conclude that 
x1 = x4
x2 = x3
y1 = y2
y3 = y4

Side of the square = (x2 - x1)

(x3, y3) = (x2, y2 + (x2 - x1))
               OR
(x3, y3) = (x2, y1 + (x2 - x1))         (Because y1 = y2)



(x4, y4) = (x1, y1 + (x2 - x1))
               OR
(x4, y4) = (x1, y2 + (x2 - x1))         (Because y2 = y1)