Question

dilate point s by a scale factor of $\frac{1}{2}$.

Explanation:

Step1: Find the coordinates of point \( S \)

Assume the center of dilation is \( R \). Count the horizontal distance from \( R \) to \( S \). Let's say \( R \) is at \((x_1,y_1)\) and \( S \) is at \((x_2,y_2)\). If \( R=(3,3) \) and \( S=(9,3) \) (assuming grid - based coordinates where each square is 1 unit). The vector from \( R \) to \( S \) is \(\overrightarrow{RS}=(9 - 3,3 - 3)=(6,0)\)

Step2: Apply the dilation formula

The formula for dilation with center \((x_0,y_0)\) (here \(x_0 = 3,y_0 = 3\)) and scale factor \(k=\frac{1}{2}\) is \((x,y)=(x_0 + k(x_1 - x_0),y_0 + k(y_1 - y_0))\). Substituting \(x_1 = 9,y_1 = 3,x_0 = 3,y_0 = 3,k=\frac{1}{2}\), we get \(x=3+\frac{1}{2}(9 - 3)=3 + 3=6\) and \(y=3+\frac{1}{2}(3 - 3)=3\)

Answer:

The dilated point of \( S \) with a scale factor of \(\frac{1}{2}\) centered at \( R \) is \((6,3)\)