\( P(6,-3) \). Triangle \( M N P \) is dilated by a scale factor of \( u \) with the origin as the center of dilation to create triangle \( M^{\prime} N^{\prime} P^{\prime} \). Which ordered pair represents the coordinates of the vertex \( P \) Pr? A \( (6+u,-3+u) \) B \( \left(\frac{6}{u},-\frac{3}{u}\right) \) C \( \left(6+\frac{1}{u},-3+\frac{1}{u}\right) \) D \( (6 u,-3 u) \)

To find the coordinates of vertex \( P^{\prime} \) after dilation, recall that in a dilation from the origin by a scale factor \( u \), each coordinate of the original point is multiplied by \( u \). For point \( P(6, -3) \), the coordinates after dilation become: \( P^{\prime} = (6u, -3u) \). So, the correct answer is: D \( (6u, -3u) \). Dilation can be an exciting concept to visualize, especially when you think of art! Imagine scaling up a drawing on graph paper—every point expands outward from the origin, giving you an even bigger version of your masterpiece without changing its shape! In practical applications, dilation is used in various fields, including computer graphics and architecture, to resize images or blueprints proportionally. When scaling up designs, you need to ensure that the dimensions remain consistent to maintain visual harmony in the final product!