Final answer:
Both alternatives (a) and (b) are potential results of the dilation, according to the study. We are unable to make an absolute decision between the two in the absence of more facts.
Step-by-step explanation:
To determine the effect of a dilation on a line passing through the center of a square, let's consider the properties of dilations:
When a figure is dilated by a scale factor k about the center of dilation, each point P is moved to a new point P′ such that: PP′ =k⋅OP
where OP is the distance from the center of dilation to point P.
In this case, line EF passes through the center of the square. If we dilate the square by a scale factor of two about its center, each point on line EF will move to a new location twice as far from the center.
Now let's analyze the answer choices:
a) If line E'F' is parallel to line EF and passes through point C, this is a possible outcome of dilation.
b) If line E'F' contains the points E and F, this is also a possible outcome. The points on the line will move, but the line itself will still contain those points.
c) If line E'F' is perpendicular to line EF and passes through point A, this is not a likely outcome of dilation. Dilations typically do not change the angles between lines.
d) Shifting two units to the right is not a typical outcome of dilation. Dilations involve stretching or compressing, not shifting.
So, based on the analysis, both options a) and b) are possible outcomes of the dilation. Without additional information, we cannot definitively choose between the two.