Graph the image of triangle ABC after a translation 1 unit left and 6 units up.
Understand the Problem
The question requires graphing the image of triangle ABC after applying a translation of 1 unit to the left and 6 units up. To solve this, we need to determine the new coordinates of the vertices of the triangle after the translation and then plot them on the graph.
Answer
The new coordinates of triangle ABC after translation are $(-7, 4)$, $(-5, 6)$, and $(-3, 4)$.
Answer for screen readers
The new coordinates of triangle ABC after the translation are:
- New A: $(-7, 4)$
- New B: $(-5, 6)$
- New C: $(-3, 4)$
Steps to Solve
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Identify the original coordinates First, we need to determine the original coordinates of triangle ABC. From the image:
- Point A: $(-6, -2)$
- Point B: $(-4, 0)$
- Point C: $(-2, -2)$
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Apply the translation The translation requires moving each point 1 unit left and 6 units up. To do this, we will adjust the coordinates as follows:
- For a left translation: subtract 1 from the x-coordinate.
- For an upward translation: add 6 to the y-coordinate.
Therefore, the new coordinates will be calculated as:
- New A: $(-6-1, -2+6) = (-7, 4)$
- New B: $(-4-1, 0+6) = (-5, 6)$
- New C: $(-2-1, -2+6) = (-3, 4)$
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List the new coordinates After applying the translation, the new coordinates of the vertices are:
- New A: $(-7, 4)$
- New B: $(-5, 6)$
- New C: $(-3, 4)$
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Graph the new points Finally, plot the new points on the graph at the new coordinates:
- Point (-7, 4)
- Point (-5, 6)
- Point (-3, 4)
The new coordinates of triangle ABC after the translation are:
- New A: $(-7, 4)$
- New B: $(-5, 6)$
- New C: $(-3, 4)$
More Information
When translating points on a graph, remember that the translation affects each coordinate individually. A left movement decreases the x-coordinate, while an upward movement increases the y-coordinate.
Tips
- Incorrectly applying the translation: Make sure to subtract from the x-coordinate for left movements and add to the y-coordinate for upward movements.
- Forgetting to adjust both coordinates: Always apply the translation to both x and y coordinates for each point.
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