Question

f = f 7 e 14 e
○ center f and scale factor 3
○ center f and scale factor 1/3
○ center d and scale factor 1/2
○ center d and scale factor 2

Explanation:

Step1: Identify corresponding sides

The length of \( F'E' \) is 7 and the length of \( FE \) is \( 7 + 14=21 \)? Wait, no, looking at the diagram, \( F'E' = 7 \) and \( FE' + E'E=? \) Wait, actually, \( F'E' \) is the side of the smaller trapezoid and \( FE \) (from \( F \) to \( E \)): Wait, \( F = F' \), \( E' \) is on \( FE \), with \( F'E' = 7 \) and \( E'E = 14 \), so \( FE=F'E'+E'E = 7 + 14 = 21 \)? Wait, no, maybe the smaller trapezoid \( G'D'E'F' \) is a scaled version of the larger trapezoid \( GDEF \) with center \( F \). Let's check the scale factor. The length of \( F'E' \) is 7, and the length of \( FE \) (if we consider the base) – wait, maybe the larger trapezoid has a base \( FE \) of length \( 7\times3 = 21 \)? Wait, no, the options have scale factor 3 or 1/3. Wait, the smaller trapezoid is inside the larger one, with center \( F \). So the scale factor is the ratio of the corresponding sides. The length of \( F'E' \) is 7, and if the larger trapezoid's corresponding side (from \( F \) to \( E \)) is \( 7\times3 = 21 \)? Wait, no, maybe the larger trapezoid is the image of the smaller one with scale factor 3, centered at \( F \). So the scale factor from the smaller to the larger is 3, so the transformation from the smaller to the larger is center \( F \) and scale factor 3. Let's verify: if the smaller trapezoid has a side \( F'E' = 7 \), then scaling with factor 3 from center \( F \) would make the larger side \( FE = 7\times3 = 21 \), but in the diagram, \( E'E = 14 \), so \( FE = F'E' + E'E = 7 + 14 = 21 \), which matches \( 7\times3 = 21 \). So the scale factor is 3, center \( F \).

Step2: Check the options

The first option is "center \( F \) and scale factor 3", which matches our calculation. The other options: scale factor 1/3 would make the larger side smaller, which is not the case. Center \( D \) doesn't make sense because the sides from \( D \) wouldn't correspond. So the correct option is the first one.

Answer:

A. center \( F \) and scale factor 3