A rectangle with endpoints \( A (0,0) \) , \( B (5,0) \) , \( C (5,3) \) , \( D (0,3 ) \) is plotted on the Cartesian plane. Two perpendicular lines are also plotted, as shown in the figure.

If the ratio of the area of \( \triangle \ \text{DFI} \) to the area of \( \triangle \ \text{CGH} \) is \( 1: 4\) , \( \angle \ \text{EFG} = 45^{\circ} \) and \( \overline{HB} = \overline{ID} \) , what is the intersection point of the perpendicular lines?

If the intersection point is in the form \( P(x , y) \) , submit your answer as the sum of \(x \) and \(y \) .

Again, just don't mind the lower case letters, just mind the bigger case letters.

For more problems like this, try answering this set .

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