Question
QUESTION 7
Explain the dialation using the coordinates and language to describe what happened to your house from the first location in quesiton 1, to the final location in Question 6.
Explain the dialation using the coordinates and language to describe what happened to your house from the first location in quesiton 1, to the final location in Question 6.
Answers
GPT-4o mini
To explain the dilation in terms of coordinates, we first need to understand what dilation means in mathematical terms. Dilation is a transformation that alters the size of a figure but retains its shape. This transformation can be centered around a point (often the origin) and involves a scale factor.
Let's assume the original coordinates of your house from Question 1 were (x, y). After applying a dilation transformation with a scale factor of k, the new coordinates (x', y') of your house can be calculated using the following formula:
1. \( x' = k \cdot x \)
2. \( y' = k \cdot y \)
**Example**:
- If your original coordinates were (2, 3), and we dilated them by a scale factor of 2, the new coordinates would be:
- \( x' = 2 \cdot 2 = 4 \)
- \( y' = 2 \cdot 3 = 6 \)
- Therefore, the new coordinates after dilation would be (4, 6).
**Descriptive Language**:
From the first location in Question 1 to the final location in Question 6, the transformation of my house can be described as follows:
"My house was originally located at a point represented by the coordinates (x, y). As we applied a dilation transformation with a scale factor of k, the position of my house changed remarkably. Each coordinate was stretched away from the origin by this factor, resulting in new coordinates (x', y'). The shape and orientation remained constant, but the size increased (or decreased) based on the chosen scale factor.
For instance, if my house originally stood at (2, 3) and we applied a dilation with a scale factor of 2, it expanded outward, relocating to (4, 6). Thus, while the location changed, it maintained its overall shape and proportionality, illustrating the concept of dilation effectively."
By summarizing the coordinates' transformation and using descriptive language, we can clearly convey the process and result of the dilation applied to the house's location.
Let's assume the original coordinates of your house from Question 1 were (x, y). After applying a dilation transformation with a scale factor of k, the new coordinates (x', y') of your house can be calculated using the following formula:
1. \( x' = k \cdot x \)
2. \( y' = k \cdot y \)
**Example**:
- If your original coordinates were (2, 3), and we dilated them by a scale factor of 2, the new coordinates would be:
- \( x' = 2 \cdot 2 = 4 \)
- \( y' = 2 \cdot 3 = 6 \)
- Therefore, the new coordinates after dilation would be (4, 6).
**Descriptive Language**:
From the first location in Question 1 to the final location in Question 6, the transformation of my house can be described as follows:
"My house was originally located at a point represented by the coordinates (x, y). As we applied a dilation transformation with a scale factor of k, the position of my house changed remarkably. Each coordinate was stretched away from the origin by this factor, resulting in new coordinates (x', y'). The shape and orientation remained constant, but the size increased (or decreased) based on the chosen scale factor.
For instance, if my house originally stood at (2, 3) and we applied a dilation with a scale factor of 2, it expanded outward, relocating to (4, 6). Thus, while the location changed, it maintained its overall shape and proportionality, illustrating the concept of dilation effectively."
By summarizing the coordinates' transformation and using descriptive language, we can clearly convey the process and result of the dilation applied to the house's location.