CEMC Galois, 2009

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

A square has vertices with coordinates $A(6, 9)$ , $B(12, 6)$ , $C(t, 0)$ , and $D(3, 3)$ .

(a) Determine the value of $t$ , the $x$ -coordinate of vertex $C$ .

(b) A line is drawn through $O(0, 0)$ and $D$ . This line meets $AB$ at $E$ . Determine the coordinates of $E$ .

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