Is the information sufficient 4?

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.

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For more problems like this, try answering this set .