Answer :
To determine the correct rule that describes the translation of a triangle on the coordinate plane, follow these steps:
1. Understand the Translation Description:
- The triangle is translated 4 units to the right and 3 units down.
2. Determine the Effects on the Coordinates:
- Translation Right: Moving a point to the right on the coordinate plane increases its x-coordinate by the number of units moved. Therefore, if a point [tex]\((x, y)\)[/tex] is moved 4 units to the right, the new x-coordinate will be [tex]\(x + 4\)[/tex].
- Translation Down: Moving a point down on the coordinate plane decreases its y-coordinate by the number of units moved. Therefore, if a point [tex]\((x, y)\)[/tex] is moved 3 units down, the new y-coordinate will be [tex]\(y - 3\)[/tex].
3. Combine Both Effects:
- Combining the two effects, a point [tex]\((x, y)\)[/tex] translated 4 units to the right and 3 units down will have new coordinates given by [tex]\((x + 4, y - 3)\)[/tex].
4. Match with Given Rules:
- We now identify the rule that represents these changes in coordinates correctly.
Comparing with the options provided:
- [tex]$(x, y) \rightarrow (x+3, y-4)$[/tex] indicates a translation of 3 units right and 4 units down (this does not match our translation).
- [tex]$(x, y) - (x+3, y+4)$[/tex] (this is incorrectly formatted and does not describe a translation).
- [tex]$(x, y) \rightarrow (x+4, y-3)$[/tex] indicates a translation of 4 units right and 3 units down (this matches our translation).
- [tex]$(x, y) - (x+4, y+3)$[/tex] (this is incorrectly formatted and does not describe a translation).
Therefore, the correct transformation rule that describes the translation is:
[tex]$(x, y) \rightarrow (x + 4, y - 3)$[/tex]
This matches the third option provided in the question.
1. Understand the Translation Description:
- The triangle is translated 4 units to the right and 3 units down.
2. Determine the Effects on the Coordinates:
- Translation Right: Moving a point to the right on the coordinate plane increases its x-coordinate by the number of units moved. Therefore, if a point [tex]\((x, y)\)[/tex] is moved 4 units to the right, the new x-coordinate will be [tex]\(x + 4\)[/tex].
- Translation Down: Moving a point down on the coordinate plane decreases its y-coordinate by the number of units moved. Therefore, if a point [tex]\((x, y)\)[/tex] is moved 3 units down, the new y-coordinate will be [tex]\(y - 3\)[/tex].
3. Combine Both Effects:
- Combining the two effects, a point [tex]\((x, y)\)[/tex] translated 4 units to the right and 3 units down will have new coordinates given by [tex]\((x + 4, y - 3)\)[/tex].
4. Match with Given Rules:
- We now identify the rule that represents these changes in coordinates correctly.
Comparing with the options provided:
- [tex]$(x, y) \rightarrow (x+3, y-4)$[/tex] indicates a translation of 3 units right and 4 units down (this does not match our translation).
- [tex]$(x, y) - (x+3, y+4)$[/tex] (this is incorrectly formatted and does not describe a translation).
- [tex]$(x, y) \rightarrow (x+4, y-3)$[/tex] indicates a translation of 4 units right and 3 units down (this matches our translation).
- [tex]$(x, y) - (x+4, y+3)$[/tex] (this is incorrectly formatted and does not describe a translation).
Therefore, the correct transformation rule that describes the translation is:
[tex]$(x, y) \rightarrow (x + 4, y - 3)$[/tex]
This matches the third option provided in the question.
