Question

PLEASE ANSWER

Rectangle ABCD is shown below with a line EF drawn through its center. If the rectangle is dilated using a scale factor of 2 and a line is drawn through the center of the new dilated figure, what relationship will that line have with line EF in the drawing below?

Answer 1

The line drawn through the center of the new dilated figure will be parallel to line EF in the original rectangle.

Step-by-step explanation:

The line drawn through the center of the new dilated figure will be parallel to line EF in the original rectangle. This is because dilation is a geometric transformation that preserves parallel lines. Since line EF is a diagonal of the rectangle, it connects opposite corners. When the rectangle is dilated, the new line through the center will still connect opposite corners, resulting in a parallel line to EF.

Answer 2

The new line will be perpendicular to line EF because both the lines are drawn through the center of the figures (rectangle ABCD and rectangle A'B'C'D') causing both of the lines to intersect each other. Rectangle ABCD will get bigger causing to form rectangle A'B'C'D' because it is dilated with a scale factor of 2. Rectangle A'B'C'D' will contain the new line and line EF.

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