What is the significance

Question

Based on your observations in Question 1 to 3, what is the significance of a dilation when 0 < n < 1? What is the significance when n = 1? What about when n > 1? Explain in terms of the size of the image and the preimage.

Answer 1

Myragu,

 

A dilation is a transformation of a geometric object which changes its size but not its shape. (See reference link included below.)

 

As you have not included any precise details about what n is, I can only assume that n is the scaling factor. If I am wrong, please reply with the correct definition of n.

 

If n > 1, then the dilation will make the object larger. For example, if a triangle is scaled by a factor of n, the sides of the transformed object will be multiplied by n, the area by n², and the volume by n³ (if the object sits in three dimensional space).

 

Similarly, if 0 < n < 1, then the object will shrink in size by this factor.

 

Examples: Starting with an equilateral triangle (all equal sides),

 

If n = 2, the sides of the triangle will double in length and the area will be multiplied by 4.

If n = ½, the sides of the triangle will be half as much and the area will by multiplied by ¼.

 

I hope this answers your question. If my initial assumption was wrong, please be sure to let me know.

 

Reference Link: www.regentsprep.org/regents/math/geometry/gt3/ldilate2.htm