Contoh Soal Dilatasi Vertikal dan Horizontal Kelas 11 | Soal Transformasi Geometri Nomor 47

Introduction

In this tutorial, we will explore vertical and horizontal dilation in geometry, specifically tailored for high school students studying transformations. Understanding these concepts is crucial for solving various geometry problems. This guide will break down the key principles of dilation and provide examples to help solidify your understanding.

Step 1: Understanding Dilation

Dilation is a transformation that alters the size of a geometric figure while maintaining its shape. This can be done vertically or horizontally.

• Vertical Dilation: Changes the height of the figure.
• Horizontal Dilation: Changes the width of the figure.

Practical Tip

• Dilation is defined by a scale factor (k):
  • If k > 1, the figure enlarges.
  • If 0 < k < 1, the figure shrinks.

Step 2: Identifying the Scale Factor

To apply dilation, you need to determine the scale factor.

1. Find the original coordinates of the points in the figure.
2. Decide on the scale factor:
   • For vertical dilation, use the formula:
     New y = k * Original y
   • For horizontal dilation, use the formula:
     New x = k * Original x

Example

• Given a point (2, 3) and a scale factor of 2 for vertical dilation:
  • New coordinates: (2, 2 * 3) = (2, 6)

Step 3: Calculating New Coordinates

Once you have the scale factor, calculate the new coordinates for each point.

• For each point (x, y):
  • Vertical dilation: (x, k * y)
  • Horizontal dilation: (k * x, y)

Example

For a horizontal dilation with a scale factor of 0.5:

• Original point: (4, 5)
• New coordinates: (0.5 * 4, 5) = (2, 5)

Step 4: Graphing the Dilation

After calculating the new coordinates, plot both the original and the dilated figures on a graph.

1. Mark the original points on the graph.
2. Mark the new points based on your calculations.
3. Draw the figures to visualize the transformation.

Common Pitfall

• Ensure you apply the scale factor correctly to either the x or y coordinate depending on whether you are performing horizontal or vertical dilation.

Conclusion

In this tutorial, we covered the essentials of vertical and horizontal dilation in geometry, including how to identify the scale factor, calculate new coordinates, and graph the results. As you practice these concepts, you'll find them beneficial for tackling more complex geometry problems. For further study, consider exploring more advanced transformations and their applications in real-world scenarios.