To determine the two moves that could replace the one translation from triangle LOW to triangle L"O"W", we need to analyze the coordinates of the points in both triangles.
Triangle LOW:
- Point L: \((-5, -2)\)
- Point O: \((-2, -4)\)
- Point W: \((-4, -6)\)
Triangle L"O"W":
- Point L": \((-5, 10)\)
- Point O": \((-2, 8)\)
- Point W": \((-4, 6)\)
Translation Analysis
To determine the translation vector, we can look at the coordinates L to L", O to O", and W to W":
-
For Point L to L":
- From L: \((-5, -2)\) to L": \((-5, 10)\)
- Vertical Change: \(10 - (-2) = 12\) (upward)
- Horizontal Change: \(-5 - (-5) = 0\) (no horizontal movement)
-
For Point O to O":
- From O: \((-2, -4)\) to O": \((-2, 8)\)
- Vertical Change: \(8 - (-4) = 12\) (upward)
- Horizontal Change: \(-2 - (-2) = 0\) (no horizontal movement)
-
For Point W to W":
- From W: \((-4, -6)\) to W": \((-4, 6)\)
- Vertical Change: \(6 - (-6) = 12\) (upward)
- Horizontal Change: \(-4 - (-4) = 0\) (no horizontal movement)
Conclusion on Moves
From this analysis, we observe that all points are moved vertically upwards by 12 units while maintaining their horizontal coordinates.
Alternative Moves Instead of a Single Translation:
-
Move each point vertically up by 6 units:
- From \((-5, -2)\) to \((-5, 4)\)
- From \((-2, -4)\) to \((-2, 2)\)
- From \((-4, -6)\) to \((-4, 0)\)
-
Move each point vertically up by another 6 units:
- From \((-5, 4)\) to \((-5, 10)\)
- From \((-2, 2)\) to \((-2, 8)\)
- From \((-4, 0)\) to \((-4, 6)\)
So, the two moves that can replace the single translation are:
- A vertical translation up by 6.
- Another vertical translation up by 6.
These two vertical moves together effectively create the same overall transformation as the single translation.
1 answer