4. A figure is dilated by a factor of \( 3 / 4 \). By what factor will the area of the figure change? \( 3 / 4 \) \( 3 / 2 \) \( 9 / 16 \) 1

When a figure is dilated, the area changes by the square of the dilation factor. So, if the figure is dilated by \( \frac{3}{4} \), the area changes by \( \left(\frac{3}{4}\right)^2 = \frac{9}{16} \). This means the area of the figure will become \( \frac{9}{16} \) of its original size! To visualize this, think about a square. If each side is reduced to three-fourths of its length, not only does the size shrink, but the area diminishes more significantly – specifically to 56.25% of the original area. It's a neat little math trick that shows how powerful scaling can be!