2. A figure is dilated by a factor of 5 . By what factor will the area of the figure change? 1 5 10 25

When a figure is dilated by a scale factor, the area of the figure changes by the square of that scale factor. So, if the figure is dilated by a factor of 5, the area will change by \(5^2\), which equals 25. Therefore, the area of the figure will increase by a factor of 25. This is a neat aspect of geometry: as you scale up (or down) a shape, while the dimensions change linearly, the area changes quadratically! Just imagine inflating a balloon – it grows in size much faster than the initial stretch of the rubber!