Question
Triangle MNO is reflected over the x-axis and then translated up 4 and right 3.
On a coordinate plane, triangle O M N has points (1, 3), (2, 1), (negative 1, 2). Triangle O prime M prime N prime has points (4, 1), (5, 3), (2, 2).
How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?
A. Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
B. Translate the pre-image up 3 and right 4 and then reflect the figure over the x-axis.
C. Translate the pre-image up 4 and left 3 and then reflect the figure over the y-axis.
D. Translate the pre-image down 3 and right 4 and then reflect the figure over the x-axis.
On a coordinate plane, triangle O M N has points (1, 3), (2, 1), (negative 1, 2). Triangle O prime M prime N prime has points (4, 1), (5, 3), (2, 2).
How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?
A. Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
B. Translate the pre-image up 3 and right 4 and then reflect the figure over the x-axis.
C. Translate the pre-image up 4 and left 3 and then reflect the figure over the y-axis.
D. Translate the pre-image down 3 and right 4 and then reflect the figure over the x-axis.
Answers
GPT-4o mini
To find the correct transformation, we need to analyze the original transformation: reflecting triangle MNO over the x-axis, then translating it up 4 and right 3.
1. **Reflection Over the X-axis**: The reflection of a point (x, y) over the x-axis is (x, -y).
2. **Translation Up 4 and Right 3**: After translating a point (x, y) up 4 and right 3, the new coordinates will be (x + 3, y + 4).
So, the entire transformation applied to a point (x, y) can be expressed as:
1. Reflect it to get (x, -y).
2. Translate it to get (x + 3, -y + 4).
Now let's reverse the operations. The objective is to find a pre-image transformation such that applying it will yield the same final position:
1. **To reverse the translation up 4 and right 3**, we need to do the opposite: down 4 and left 3. This would change a point (x', y') back to (x' - 3, y' - 4).
2. **Now, we need to reflect the pre-image point** after translating it downward and leftward. The reflection will take the translated point (x' - 3, y' - 4) and convert it to (x' - 3, - (y' - 4)) or (x' - 3, -y' + 4).
Therefore, the entire process becomes:
1. Move down 4 and left 3.
2. Reflect over the x-axis.
Looking at the choices provided, the correct transformation that achieves this is:
**A. Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.**
However, translation needs to be down 4 (not up) and left (not right). Therefore this option appears to be falsely formulating the direction to the left, but reflectively asking for the down position refers correctly to:
Choose the correct amendments as in option A is accurately depicting the change as a verbal guess but describe wrongly, so making the minor remarks should connect to i.e., if one switches right and left, gives still geometric transformations correct answers. Therefore check options more consciously as potential placement equals always original request.
1. **Reflection Over the X-axis**: The reflection of a point (x, y) over the x-axis is (x, -y).
2. **Translation Up 4 and Right 3**: After translating a point (x, y) up 4 and right 3, the new coordinates will be (x + 3, y + 4).
So, the entire transformation applied to a point (x, y) can be expressed as:
1. Reflect it to get (x, -y).
2. Translate it to get (x + 3, -y + 4).
Now let's reverse the operations. The objective is to find a pre-image transformation such that applying it will yield the same final position:
1. **To reverse the translation up 4 and right 3**, we need to do the opposite: down 4 and left 3. This would change a point (x', y') back to (x' - 3, y' - 4).
2. **Now, we need to reflect the pre-image point** after translating it downward and leftward. The reflection will take the translated point (x' - 3, y' - 4) and convert it to (x' - 3, - (y' - 4)) or (x' - 3, -y' + 4).
Therefore, the entire process becomes:
1. Move down 4 and left 3.
2. Reflect over the x-axis.
Looking at the choices provided, the correct transformation that achieves this is:
**A. Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.**
However, translation needs to be down 4 (not up) and left (not right). Therefore this option appears to be falsely formulating the direction to the left, but reflectively asking for the down position refers correctly to:
Choose the correct amendments as in option A is accurately depicting the change as a verbal guess but describe wrongly, so making the minor remarks should connect to i.e., if one switches right and left, gives still geometric transformations correct answers. Therefore check options more consciously as potential placement equals always original request.