Activity A boat dealer's logo needs to be resized depending on the space available in the advertisement. You will use the GeoGeb
ra geometry tool to resize the logo. To get started, go to dilations C. Then complete each step below. If you need help, follow these instructions for using GeoGebra. You can control the size of the sailboat by moving the slider on the screen. The value n set by the slider bar is the scale factor of the dilation. The center of dilation is the origin, or polnt). Question 1 Vary the scale factor n from values less than 1 to values greater than 1. How do the points in the resulting Images differ from the corresponding points on the preimage? Describe the general location of the points relative to the center of dilation. What happens to the logo of the sailboat as you vary the scale factor?
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Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).
Given:
The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).
The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).
To find:
The algebraic representation that represents this dilation.
Solution:
If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:
...(i)
Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,
The image of G after dilation is G'(5,-5). So,
On comparing both sides, we get
So, the scale factor is .
Substituting in (i), we get
Therefore, the required algebraic representation to represents this dilation is .