To graph the image of triangle XYZ after a translation of 3 units left and 4 units up, we need to apply the translation to each point of the original triangle. Here's how you can do it:
1. Original Triangle XYZ:
- Given the original triangle XYZ with coordinates:
- X(-6, 1), Y(-3, -2), Z(-4, 5).
2. Translation of 3 units left and 4 units up:
- To translate each point of the original triangle, we subtract 3 from the x-coordinates (move left) and add 4 to the y-coordinates (move up).
3. Coordinates of X'Y'Z' after Translation:
- X' = X - 3 = (-6 - 3, 1 + 4) = (-9, 5)
- Y' = Y - 3 = (-3 - 3, -2 + 4) = (-6, 2)
- Z' = Z - 3 = (-4 - 3, 5 + 4) = (-7, 9)
4. Graphing the Image:
- Plot the points X'(-9, 5), Y'(-6, 2), Z'(-7, 9) on the coordinate plane.
- Connect these points to form the image triangle X'Y'Z'.
5. Conclusion:
- By applying a translation of 3 units left and 4 units up to each point of the original triangle XYZ, we obtained the image triangle X'Y'Z' with coordinates X'(-9, 5), Y'(-6, 2), Z'(-7, 9). This represents the new position of the triangle after the translation.
