# Is the information sufficient 4?

Geometry Level 3

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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