Option (4) will be the correct option.
Given in the question,
- ABCD is dilated by a scale factor of 2 about point E.
- A'B'C'D' is the dilated figure.
Option (1). E'F' is perpendicular to EF.
Since, center of dilation of ABCD is at E, E' will coincide point E.
Therefore, EF and E'F' can't be perpendicular.
Option (2). E'F' is parallel to EF.
Since, center of dilation of ABCD is at E, point E' will coincide point E.
Therefore, E'F' can't be parallel.
Option (3). E'F' intersects with point B'.
Since, center of dilation of ABCD is at E, EF will lie on E'F'.
Therefore, E'F' cant intersect point B'.
Option (4). E'F' passes through center of dilation.
Since, center of dilation of ABCD is at E, therefore, E'F' will pass through the center of dilation E.
Therefore, Option (4) is the correct option.
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