Question

which figure is a dilation of figure a with the center of dilation at point e? figure b figure c figure d

Explanation:

Dilation is a transformation that scales a figure by a scale factor relative to a center point (here, \( E \)). For a dilation, the lines from the center \( E \) to corresponding vertices of the original and dilated figures should be collinear, and the ratios of distances from \( E \) to each vertex should be constant (scale factor).

• Figure \( A \) is a small square. Checking each figure:
• Figure \( B \): The lines from \( E \) to \( B \)'s vertices don't maintain the same scale ratio as \( A \) (visually, the scaling isn't consistent with a single factor from \( E \)).
• Figure \( C \): The lines from \( E \) to \( C \)'s vertices are collinear with \( A \)'s vertices when extended from \( E \), and the scale factor (ratio of distances from \( E \)) is consistent (e.g., if \( A \) has side length \( 1 \) from \( E \)-related points, \( C \) has a larger but proportional length).
• Figure \( D \): The shape and scaling from \( E \) don't match the dilation criteria (the proportions relative to \( E \) aren't consistent with \( A \)).

Answer:

figure \( C \)