Question
A dilation centered at the origin with a scale factor of is applied to .
The result is , as shown below.
y24681012-2-4-6-8-10-12x24681012-2-4-6-8-10-12
(a)The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks to give the coordinates after the dilation.
original coordinates final coordinates
(b)Choose the general rule below that describes the dilation mapping to .
The result is , as shown below.
y24681012-2-4-6-8-10-12x24681012-2-4-6-8-10-12
(a)The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks to give the coordinates after the dilation.
original coordinates final coordinates
(b)Choose the general rule below that describes the dilation mapping to .
Answers
Answered by
GPT-4o mini
To provide specific answers to your questions, I need additional details. However, based on the concept of dilation centered at the origin, here's how we typically fill in the information:
(a) When a dilation centered at the origin is applied, the coordinates of the points are transformed according to the scale factor \( k \). The formula for dilation is:
\[
(x, y) \to (kx, ky)
\]
To fill in the blanks for the original and final coordinates, we need to know the original coordinates and the scale factor. Please provide that information.
(b) The general rule for the dilation mapping \( (x, y) \) to \( (kx, ky) \) could be one of the following forms, depending on the scale factor \( k \):
- If \( k > 1 \), the mapping expands the figure.
- If \( 0 < k < 1 \), the mapping reduces the figure.
Typically, a general rule for the dilation would look like this:
- For example, if \( k = 3 \), it would be \( (x, y) \to (3x, 3y) \).
- If \( k = 1/2 \), it would be \( (x, y) \to \left(\frac{1}{2}x, \frac{1}{2}y\right) \).
Again, please provide the scale factor or original coordinates for more tailored responses.
(a) When a dilation centered at the origin is applied, the coordinates of the points are transformed according to the scale factor \( k \). The formula for dilation is:
\[
(x, y) \to (kx, ky)
\]
To fill in the blanks for the original and final coordinates, we need to know the original coordinates and the scale factor. Please provide that information.
(b) The general rule for the dilation mapping \( (x, y) \) to \( (kx, ky) \) could be one of the following forms, depending on the scale factor \( k \):
- If \( k > 1 \), the mapping expands the figure.
- If \( 0 < k < 1 \), the mapping reduces the figure.
Typically, a general rule for the dilation would look like this:
- For example, if \( k = 3 \), it would be \( (x, y) \to (3x, 3y) \).
- If \( k = 1/2 \), it would be \( (x, y) \to \left(\frac{1}{2}x, \frac{1}{2}y\right) \).
Again, please provide the scale factor or original coordinates for more tailored responses.