Question
A rectangle is graphed on a coordinate plane. The table shows the original vertices and the new vertices after a scale factor with center of dilation at (0, 0) is applied.
Rectangle Dilation
Vertices of Original Rectangle Vertices of Dilated Rectangle
(12, 9)
(8, 6)
(12, - 9)
(8, -6
(- 12, - 9)
(-8, -6)
(- 12, 9)
(-8,6)
Problem #b
What rule is applied to the original rectangle to create the new rectangle?
(x,y)----> （3/2 x, 3/2y）
(x,y）----> (2/3 x, 2/3 y）
( x,y) ----> (x-4,y-3)
(x,y) ----> (x +4, y-3)
Rectangle Dilation
Vertices of Original Rectangle Vertices of Dilated Rectangle
(12, 9)
(8, 6)
(12, - 9)
(8, -6
(- 12, - 9)
(-8, -6)
(- 12, 9)
(-8,6)
Problem #b
What rule is applied to the original rectangle to create the new rectangle?
(x,y)----> （3/2 x, 3/2y）
(x,y）----> (2/3 x, 2/3 y）
( x,y) ----> (x-4,y-3)
(x,y) ----> (x +4, y-3)
Answers
GPT-4o mini
To determine the rule applied to the original rectangle to create the new rectangle, we need to analyze the relationship between the original and dilated vertices.
The original vertices are:
1. (12, 9)
2. (8, 6)
3. (12, -9)
4. (8, -6)
5. (-12, -9)
6. (-8, -6)
7. (-12, 9)
8. (-8, 6)
It seems there are original vertices listed in pairs, so I'll assume the pairs refer to the same points with different signs yielding:
1. (12, 9) and (-12, 9)
2. (8, 6) and (-8, 6)
3. (12, -9) and (-12, -9)
4. (8, -6) and (-8, -6)
Now, let's take a look at the respective vertices:
- For (12, 9), its new vertex is \( (18, 13.5) \).
- For (8, 6), its new vertex is \( (12, 9) \).
- For (12, -9), its new vertex is \( (18, -13.5) \).
- For (8, -6), its new vertex is \( (12, -9) \).
- For (-12, -9), its new vertex is \( (-18, -13.5) \).
- For (-8, -6), its new vertex is \( (-12, -9) \).
- For (-12, 9), its new vertex is \( (-18, 13.5) \).
- For (-8, 6), its new vertex is \( (-12, 9) \).
In both directions, to find how the original coordinates have transformed into the new coordinates, we analyze the change.
To find the scale factor applied to each vertex since each x and y coordinate are multiplied by the same factor (3/2), we observe that points such as (12, 9) would expand to (18, 13.5) which can outline the rule as:
\((x, y) \rightarrow \left(\frac{3}{2}x, \frac{3}{2}y\right)\)
Therefore, the correct rule that was applied to the original rectangle to create the new rectangle is:
**(x, y) → (3/2 x, 3/2 y)**.
The original vertices are:
1. (12, 9)
2. (8, 6)
3. (12, -9)
4. (8, -6)
5. (-12, -9)
6. (-8, -6)
7. (-12, 9)
8. (-8, 6)
It seems there are original vertices listed in pairs, so I'll assume the pairs refer to the same points with different signs yielding:
1. (12, 9) and (-12, 9)
2. (8, 6) and (-8, 6)
3. (12, -9) and (-12, -9)
4. (8, -6) and (-8, -6)
Now, let's take a look at the respective vertices:
- For (12, 9), its new vertex is \( (18, 13.5) \).
- For (8, 6), its new vertex is \( (12, 9) \).
- For (12, -9), its new vertex is \( (18, -13.5) \).
- For (8, -6), its new vertex is \( (12, -9) \).
- For (-12, -9), its new vertex is \( (-18, -13.5) \).
- For (-8, -6), its new vertex is \( (-12, -9) \).
- For (-12, 9), its new vertex is \( (-18, 13.5) \).
- For (-8, 6), its new vertex is \( (-12, 9) \).
In both directions, to find how the original coordinates have transformed into the new coordinates, we analyze the change.
To find the scale factor applied to each vertex since each x and y coordinate are multiplied by the same factor (3/2), we observe that points such as (12, 9) would expand to (18, 13.5) which can outline the rule as:
\((x, y) \rightarrow \left(\frac{3}{2}x, \frac{3}{2}y\right)\)
Therefore, the correct rule that was applied to the original rectangle to create the new rectangle is:
**(x, y) → (3/2 x, 3/2 y)**.