3.2 and. 4.8 what is the scale factor of dilation
The Correct Answer and Explanation is:
To determine the scale factor of dilation between two numbers, 3.2 and 4.8, we compare the second value (4.8) to the first value (3.2). The scale factor can be calculated using the formula:
[
\text{Scale Factor} = \frac{\text{New Value}}{\text{Original Value}}
]
Calculation:
[
\text{Scale Factor} = \frac{4.8}{3.2} = 1.5
]
The scale factor of dilation is 1.5.
Explanation:
A scale factor is a number that describes how much an object or value is enlarged or reduced in size. In this case, the numbers 3.2 and 4.8 represent two corresponding values, where 4.8 is the new value, and 3.2 is the original value.
Step-by-Step Process:
- Understand Dilation:
Dilation in mathematics refers to resizing a figure or value by a specific ratio while maintaining its proportionality. The scale factor represents this ratio. - Identify Values:
Here, 3.2 is the original value (before dilation), and 4.8 is the new value (after dilation). - Divide New by Original:
To find the scale factor, divide the new value (4.8) by the original value (3.2). This calculation gives a result of 1.5. - Interpret the Result:
A scale factor greater than 1 (1.5 in this case) indicates enlargement. This means the value increased by 50% compared to the original.
Application:
Understanding scale factors is essential in various fields like geometry, where shapes are resized while maintaining their proportions, or in real-life situations like resizing images or models.
The scale factor of 1.5 means that every unit in the original (3.2) was multiplied by 1.5 to produce the enlarged value (4.8). Conversely, dividing the new value (4.8) by 1.5 would yield the original value (3.2), confirming the correctness of the calculation.