Question
If this rectangle is dilated using a scale factor of One-half through point B, what is the result?
Point B is the bottom left corner of rectangle X.
Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X.
Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner.
Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X and is outside of rectangle X.
Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and is outside of rectangle X.
Point B is the bottom left corner of rectangle X.
Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X.
Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner.
Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X and is outside of rectangle X.
Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and is outside of rectangle X.
Answers
GPT-4o mini
To analyze the scenario, let's first clarify the details:
1. Rectangle X has a bottom left corner at point B.
2. A dilation with a scale factor of one-half means that every point on the rectangle is moved closer to point B, reducing its size to half.
3. The term "rectangle X prime" refers to the new shape created after the dilation.
Now, let's go through the possibilities you've provided based on this information:
- **Rectangle X prime is double the size of rectangle X.** This contradicts the dilation by a scale factor of one-half. Therefore, this option is incorrect.
- **Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner.** This describes the correct result of dilation using a scale factor of one-half centered at point B, as the new rectangle would indeed be half the original size and retain its position with point B remaining the bottom left corner. This option is correct.
- **Rectangle X prime is double the size of rectangle X and is outside of rectangle X.** Like the first option, this contradicts the dilation by a scale factor of one-half and is incorrect.
- **Rectangle X prime is half the size of rectangle X and is outside of rectangle X.** This is also incorrect because the dilation would not reposition the rectangle to be outside of rectangle X; point B remains the bottom left corner.
In conclusion, the correct result after dilating rectangle X by a scale factor of one-half through point B is:
**Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner.**
1. Rectangle X has a bottom left corner at point B.
2. A dilation with a scale factor of one-half means that every point on the rectangle is moved closer to point B, reducing its size to half.
3. The term "rectangle X prime" refers to the new shape created after the dilation.
Now, let's go through the possibilities you've provided based on this information:
- **Rectangle X prime is double the size of rectangle X.** This contradicts the dilation by a scale factor of one-half. Therefore, this option is incorrect.
- **Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner.** This describes the correct result of dilation using a scale factor of one-half centered at point B, as the new rectangle would indeed be half the original size and retain its position with point B remaining the bottom left corner. This option is correct.
- **Rectangle X prime is double the size of rectangle X and is outside of rectangle X.** Like the first option, this contradicts the dilation by a scale factor of one-half and is incorrect.
- **Rectangle X prime is half the size of rectangle X and is outside of rectangle X.** This is also incorrect because the dilation would not reposition the rectangle to be outside of rectangle X; point B remains the bottom left corner.
In conclusion, the correct result after dilating rectangle X by a scale factor of one-half through point B is:
**Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner.**