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A triangle with coordinates (6, 4), (2, −1), and (−3, 5) is translated 4 units left and rotated 180° about the origin. What are the coordinates of its image?

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Edufirst

Answer:

The coordinates of the image are:

  • (-2, -4)
  • (2, 1)
  • (5, 5)

Explanation:

1. Translation 4 units left

A translation 4 units left does not change the y-coordinate of the points and reduces the x-coordinate 4 units.

The rule is: (x,y) → (x-4,y)

Apply that rule to the three vertices of the triangle:

  • (6, 4) → (6 - 4, 4) = (2, 4)
  • (2, −1) → (2 - 4, -1) = (-2, -1)
  • (−3, 5) → (-3 - 2, 5) = (-5, -5)

2. Rotation 180° about the origin

A rotation 180º about the origin negates both coordinates, x and y.

The rule is: (x,y) → (-x, -y)

Apply that rule to the images after the translation 4 units left:

  • (2, 4) → (-2, -4)
  • (-2, -1) → (2, 1)
  • (-5, -5) → (5, 5)

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