Geometric Transformation Ff54Ca

1. **Stating the problem:** We want to understand the quick formulas (rumus cepat) for geometric transformations. 2. **Types of geometric transformations:** The main types are translation, rotation, reflection, and dilation (scaling). 3. **Translation formula:** Moves a point $(x,y)$ by $(a,b)$ to $(x',y')$: $$x' = x + a$$ $$y' = y + b$$ 4. **Rotation formula:** Rotating a point $(x,y)$ about the origin by an angle $\theta$: $$x' = x\cos\theta - y\sin\theta$$ $$y' = x\sin\theta + y\cos\theta$$ 5. **Reflection formula:** Reflecting a point $(x,y)$ about the x-axis or y-axis: - About x-axis: $$x' = x, \quad y' = -y$$ - About y-axis: $$x' = -x, \quad y' = y$$ 6. **Dilation (scaling) formula:** Scaling a point $(x,y)$ by a factor $k$ from the origin: $$x' = kx$$ $$y' = ky$$ 7. **Summary:** These formulas allow quick calculation of new coordinates after transformations. This completes the explanation of quick formulas for geometric transformations.