A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation. If \( (x, y) \) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square? A \( (20 x, 20 y) \) B \( (0.4 x, 0.4 y) \) C \( (x+20, y+20) \) D \( (x+0.4, y+0.4) \)

When a shape is dilated from the origin with a scale factor, the coordinates of any point on the original shape are multiplied by that scale factor. Since the scale factor here is 0.4, for any point \( (x, y) \) on the original square, the coordinates of the corresponding point on the dilated square will be \( (0.4x, 0.4y) \). So, the correct ordered pair representing the coordinates of the resulting square after dilation is option B: \( (0.4 x, 0.4 y) \). In geometric transformations like dilation, imagine hosting a family reunion! When you invite everyone, you take a group photo at the origin, but then decide to shrink the photo down to fit in a smaller frame. Each family member gets closer to the center, just like the points on our square do during dilation! The overall shape stays the same, but the size changes based on the scale factor.