\(ABCD\) is a square. The equations of \(AB\), \(AD\) and \(BD\) are \(y = 0\), \(x = 0\) and \(x + y - 4 = 0\) respectively. What is the equation of \(AC\)?
\(x-y=0\)
Solving \(y=0\) and \(x=0\) gives \(A=(0,0)\). Solving \(y=0\) with \(x+y-4=0\) gives \(B=(4,0)\), and solving \(x=0\) with \(x+y-4=0\) gives \(D=(0,4)\). Since \(ABCD\) is a square, \(C=B+D-A=(4,4)\). The diagonal \(AC\) joins \((0,0)\) and \((4,4)\), giving \(x-y=0\).
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