Answer:
See below
Step-by-step explanation:
Vector argument
Vector DF is (5, -4) - (5, 5) = (0, -9).
Vector EG is (2, 2) - (8, 2) = (-6, 0).
The dot-product of these two vector is (0, -9)•(-6, 0) = 0·(-6) + (-9)·0 = 0.
When the dot-product of two vectors is zero, those vectors are at right-angles to each other. Therefore diagaonal DF ⊥ diagonal EG.
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Alternate argument
The x-coordinates of points D and F are the same, so diagonal DF is a vertical line. The y-coordinates of points E and G are the same, so diagonal EG is a horizontal line. Vertical lines are perpendicular to horizontal lines, so DF ⊥ EG.
