Give the coordinates of \( S \) under a dilation about point \( P \) with scale factor \( \frac{7}{2} \). \( S(-4,5) \) \( P(4,2) \) Your answer

To find the coordinates of \( S \) under a dilation about point \( P \) with a scale factor of \( \frac{7}{2} \), we can use the formula for dilation centered at a point. The formula for new coordinates \( S' \) is: \[ S' = P + k(S - P) \] where \( k \) is the scale factor. Let's break it down. 1. First, find the vector \( S - P \): \[ S - P = (-4 - 4, 5 - 2) = (-8, 3) \] 2. Now multiply this vector by the scale factor \( \frac{7}{2} \): \[ k(S - P) = \frac{7}{2} \cdot (-8, 3) = \left(-28, \frac{21}{2}\right) \] 3. Now add this to the point \( P \): \[ S' = P + k(S - P) = (4, 2) + \left(-28, \frac{21}{2}\right) = \left(4 - 28, 2 + \frac{21}{2}\right) = (-24, 2 + 10.5) = (-24, 12.5) \] Therefore, the coordinates of \( S' \) are \( (-24, 12.5) \).