Question
On the coordinate plane, point B is translated to point B'. Which functions describe the two translations? (1 point) Responses f(x) = x - 16 and g(y) = y + 12 f(x) = x - 16 and g(y) = y + 12 f(x) = x - 6 and g(y) = y + 2 f(x) = x - 6 and g(y) = y + 2 f(x) = 6 - x and g(y) = 2 + y f(x) = 6 - x and g(y) = 2 + y f(x) = x + 6 and g(y) = y - 2
Answers
GPT-4o mini
To determine which functions describe the translation from point B to point B', we need to analyze how the coordinates of point B change to reach the coordinates of point B'.
Let's denote point B as (x, y). A translation will change the x-coordinate by a certain amount and the y-coordinate by some other amount.
1. When the translation function for x is \( f(x) \) and for y is \( g(y) \), we assess how these functions modify point B:
- If \( f(x) = x - 16 \), then the x-coordinate has been translated left by 16 units.
- If \( g(y) = y + 12 \), then the y-coordinate has been translated up by 12 units.
- This means point B translates to \( (x - 16, y + 12) \).
2. If \( f(x) = x - 6 \) and \( g(y) = y + 2 \):
- This translates the x-coordinate left by 6 units and the y-coordinate up by 2 units, resulting in a new point at \( (x - 6, y + 2) \).
3. For \( f(x) = 6 - x \) and \( g(y) = 2 + y \):
- The function \( 6 - x \) indicates a reflection over the line \( x = 3 \), and \( g(y) = 2 + y \) indicates a translation upward by 2 units.
4. Finally, if \( f(x) = x + 6 \) and \( g(y) = y - 2 \):
- This translates the x-coordinate right by 6 units and the y-coordinate down by 2 units.
To determine the correct pair of functions from the translations provided, you need to know the specifics of point B and point B' (i.e., how much B moves to become B'). Without that specific information, we can only evaluate the translations abstractly.
If you can provide the coordinates of point B and point B', I can help identify the actual correct translation functions.
Let's denote point B as (x, y). A translation will change the x-coordinate by a certain amount and the y-coordinate by some other amount.
1. When the translation function for x is \( f(x) \) and for y is \( g(y) \), we assess how these functions modify point B:
- If \( f(x) = x - 16 \), then the x-coordinate has been translated left by 16 units.
- If \( g(y) = y + 12 \), then the y-coordinate has been translated up by 12 units.
- This means point B translates to \( (x - 16, y + 12) \).
2. If \( f(x) = x - 6 \) and \( g(y) = y + 2 \):
- This translates the x-coordinate left by 6 units and the y-coordinate up by 2 units, resulting in a new point at \( (x - 6, y + 2) \).
3. For \( f(x) = 6 - x \) and \( g(y) = 2 + y \):
- The function \( 6 - x \) indicates a reflection over the line \( x = 3 \), and \( g(y) = 2 + y \) indicates a translation upward by 2 units.
4. Finally, if \( f(x) = x + 6 \) and \( g(y) = y - 2 \):
- This translates the x-coordinate right by 6 units and the y-coordinate down by 2 units.
To determine the correct pair of functions from the translations provided, you need to know the specifics of point B and point B' (i.e., how much B moves to become B'). Without that specific information, we can only evaluate the translations abstractly.
If you can provide the coordinates of point B and point B', I can help identify the actual correct translation functions.