Transformasi Geometri [Part 4] - Dilatasi

Summary

In this educational video, Pak Beni introduces the concept of dilatation in geometry. He explains how dilatation is a transformation that alters the size of a figure based on a scale factor, either enlarging or shrinking it. The video covers the formula for dilatation and provides practical examples, demonstrating how to calculate new coordinates by multiplying the original coordinates with the scale factor. Pak Beni also clarifies key points such as the center of dilatation and how different values of the scale factor affect the transformation. The video concludes with practice problems to reinforce understanding.

Takeaways

• 😀 Dilatation is a geometric transformation that changes the size of a shape by scaling every point, either enlarging or reducing it.
• 😀 The two key factors in dilation are the scaling factor (k) and the center of dilation (often the origin, 0,0).
• 😀 The scaling factor (k) can be greater than 1 (which enlarges the shape) or between 0 and 1 (which reduces the shape).
• 😀 Dilating a shape involves multiplying the coordinates of each point by the scaling factor relative to the center of dilation.
• 😀 For example, if a point (2, 1) is dilated with a scaling factor of 2, the new coordinates become (4, 2).
• 😀 A dilation with a scaling factor of 2 makes the shape grow by a factor of two times its original size.
• 😀 A dilation with a scaling factor of 1/2 reduces the size of the shape, as seen in the shrinking of a triangle.
• 😀 The general formula for dilation is: P' = (k * x, k * y), where (x, y) are the coordinates of a point and k is the scaling factor.
• 😀 If the scaling factor is negative, the shape is not only resized but also reflected across the origin.
• 😀 In example problems, the scaling factor and the center of dilation (0,0) are used to calculate the coordinates of the dilated shape.
• 😀 Practice problems allow students to apply the concept of dilation, calculate new coordinates, and understand the effect of different scaling factors.

Q & A

What is dilatation in geometry?

Dilatation is a transformation that changes the size of a geometric figure by multiplying its coordinates by a scale factor relative to a specific center point, usually the origin (0,0). This transformation can either enlarge or shrink the figure.

How does the scale factor affect the size of the geometric figure?

If the scale factor is greater than 1, the figure enlarges. If the scale factor is between 0 and 1 (a fraction), the figure shrinks.

What are the two key elements that influence dilatation?

The two key elements are the scale factor and the center of dilatation. The scale factor determines the magnitude of the change in size, while the center of dilatation is the point from which the transformation is applied.

In Pak Beni's example, what happens when the scale factor is 2?

When the scale factor is 2, the coordinates of each point on the figure are multiplied by 2, effectively enlarging the figure to double its original size.

How can we calculate the new coordinates after dilatation?

To calculate the new coordinates, multiply the original coordinates by the scale factor. For example, if the original coordinates are (x, y) and the scale factor is 2, the new coordinates will be (2x, 2y).

What does it mean if the scale factor is a fraction, like 1/2 or 2/3?

If the scale factor is a fraction between 0 and 1, the figure shrinks. The coordinates of each point are multiplied by the fraction, reducing the size of the figure.

How do you determine the scale factor if the original and dilated coordinates are given?

To find the scale factor, divide the dilated coordinate by the original coordinate. For example, if the original x-coordinate is -6 and the dilated x-coordinate is 18, the scale factor is 18 ÷ -6 = -3.

What happens when the center of dilatation is located at the origin (0,0)?

When the center of dilatation is at the origin (0,0), the transformation is applied directly to the coordinates of the points, and the results depend on the scale factor.

What does Pak Beni mean by 'bayangan' in the context of dilatation?

'Bayangan' refers to the image or the transformed version of the original geometric figure after applying dilatation.

How do you handle a problem where you need to find the original coordinates based on the dilated coordinates and the scale factor?

To find the original coordinates, divide the dilated coordinates by the scale factor. For example, if the dilated x-coordinate is -8 and the scale factor is 4, the original x-coordinate would be -8 ÷ 4 = -2.