Question

unit 4 lesson 6 dllations
a dilation is a proportional increase or decrease in size in directions.
a dilation is a non - rigid transformation. dilations do not preserve distance but do preserve their angle measures.
the scale factor (k) is the ratio that describes how much the shape has been enlarged or reduced in a dilation.
if the scale factor (k) is the size of the shape does not change.
scale factor = image / preimage

Explanation:

Step1: Recall the formula for scale factor

The formula for scale factor \( k \) is \( k=\frac{\text{Image}}{\text{Pre - image}}\). This is a fundamental formula in the concept of dilation in geometry.

Step2: Analyze the property of dilation regarding shape and size

Dilation is a transformation. The shape does not change (the figures are similar, corresponding angles are equal). But the size changes. The scale factor \( k \) determines if it is an enlargement (\(k> 1\)) or a reduction (\(0 < k<1\)).

Answer:

Scale Factor \(=\frac{\text{Image}}{\text{Pre - image}}\); If the scale factor (\(k\)) is \(\frac{\text{Image}}{\text{Pre - image}}\) the size of the shape does not change (this is incorrect, actually when \(k = 1\) the size does not change, but in general \(k=\frac{\text{Image}}{\text{Pre - image}}\) describes the size change). The scale factor (\(k\)) is the ratio that describes how much the shape has been enlarged or reduced in a dilation. A dilation is a proportional increase or decrease in size in all directions. Dilation is a non - rigid transformation. Dilations do not preserve distance but do preserve their angle measures.