Geometric Transformation Math Example 2

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Example 2

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Point P(3,−1)P(3, -1) is reflected over the y-axis, then translated by (2,5)(2, 5). Find the final image.

Solution

  1. 1
    Step 1: Reflect P(3,−1)P(3,-1) over the y-axis: (x,y)→(−x,y)(x,y) \to (-x, y), giving P′(−3,−1)P'(-3, -1).
  2. 2
    Step 2: Translate P′(−3,−1)P'(-3,-1) by (2,5)(2,5): (−3+2, −1+5)=(−1,4)(-3+2,\ -1+5) = (-1, 4).
  3. 3
    Step 3: Final image: (−1,4)(-1, 4).

Answer

Final image: (−1,4)(-1, 4)
Composition of transformations means applying them one after another. The order matters — reflecting then translating generally gives a different result than translating then reflecting. Here, we reflect first (step 1), then translate (step 2).

About Geometric Transformation

A function that maps every point of a geometric figure to a new position, changing its location, orientation, or size.

Learn more about Geometric Transformation →

More Geometric Transformation Examples

Example 1 easy

Name and describe the four basic geometric transformations.

Example 3 easy

Which geometric transformations are isometries (preserve distances)?

Example 4 hard

Show that a 180° rotation about the origin is equivalent to the transformation [formula]. Verify wit

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