In the diagram, A'B'C' is an image of ABC. Which rule describes this translation? Triangle A B C has solid segments. A is at left parenthesis negative 3 comma 2 right parenthesis. B is at left parenthesis negative 3 comma negative 3 right parenthesis. C is at left parenthesis 0 comma negative 2 right parenthesis. Triangle A prime B prime C prime has dashed segments. A prime is at left parenthesis 2 comma 5 right parenthesis. B prime is at left parenthesis 2 comma 0 right parenthesis. C prime is at left parenthesis 5 comma 1 right parenthesis. (1 point) Responses (x, y)(x – 5, y – 3) ( x, y ) Image with alt text: A photo shows an arrow icon pointing to the right. ( x – 5, y – 3) (x, y)(x + 5, y + 3) ( x, y ) Image with alt text: A photo shows an arrow icon pointing to the right. ( x + 5, y + 3) (x, y)(x – 3, y – 5) ( x, y ) Image with alt text: A photo shows an arrow icon pointing to the right. ( x – 3, y – 5) (x, y)(x + 3, y + 5)
The translation rule that describes this transformation is (x + 5, y + 3).
The rule that describes this translation is: (x, y) -> (x - 3, y - 5).
To describe a translation, we need to identify the direction and distance of the movement of each point. In this case, we can see that the image (A'B'C') has moved to the right and up compared to the original triangle (ABC).
To determine the direction, we can compare the coordinates of a point in the image (A'B'C') with the corresponding point in the original triangle (ABC). Let's take point A as an example:
- In the original triangle (ABC), the coordinates of point A are (-3, 2).
- In the image (A'B'C'), the coordinates of the corresponding point A' are (2, 5).
To find the direction of the translation, we subtract the x and y coordinates of A from A':
- For the x-coordinate: 2 - (-3) = 5
- For the y-coordinate: 5 - 2 = 3
So, the x-coordinate has increased by 5, and the y-coordinate has increased by 3. This tells us that the image has moved 5 units to the right and 3 units up.
Now we can look at the answer choices:
- (x, y)(x – 5, y – 3): This describes a translation that moves 5 units to the left and 3 units down, which is the opposite direction of the given translation.
- (x, y)(x + 5, y + 3): This describes a translation that moves 5 units to the right and 3 units up, which matches the given translation.
- (x – 5, y – 3)(x, y): This describes a translation that moves 5 units to the right and 3 units up, but the coordinates are reversed compared to the given translation.
- (x – 3, y – 5)(x, y): This describes a translation that moves 3 units to the left and 5 units down, which is not the correct translation.
Therefore, the correct answer is: (x, y)(x + 5, y + 3)