Rectangle Dilation D56487

1. **State the problem:** We have rectangle ABCD and a point E inside it. We want to find the image of rectangle ABCD after dilation with center E and scale factor 3. 2. **Formula for dilation:** The coordinates of the image point $P'$ of a point $P$ under dilation with center $E$ and scale factor $k$ are given by: $$P' = E + k(P - E)$$ This means we take the vector from $E$ to $P$, multiply it by $k$, and add it back to $E$. 3. **Apply the formula:** For each vertex $A, B, C, D$ of the rectangle, calculate the image points $A', B', C', D'$: $$A' = E + 3(A - E)$$ $$B' = E + 3(B - E)$$ $$C' = E + 3(C - E)$$ $$D' = E + 3(D - E)$$ 4. **Interpretation:** This means each point moves away from $E$ by a factor of 3 along the line connecting $E$ to that point. 5. **Result:** The dilated rectangle $A'B'C'D'$ is similar to $ABCD$ but scaled by 3 times with respect to $E$. This completes the dilation process and locates the image points accordingly.