Question

Write a rule to describe each transformation.

H(−5, −4), G(−2, −1), F(0, −3) to

G'(−2, 1), F'(0, 3), H'(−5, 4)

Question 9 options:

reflection across the y-axis


translation: 2 units right and 1 unit down


rotation 180° about the origin


reflection across the x-axis

Answer 1

To determine the correct transformation for the given points, let's analyze the changes in their coordinates.

Original Points:
- H(−5, −4)
- G(−2, −1)
- F(0, −3)

Transformed Points:
- G'(−2, 1)
- F'(0, 3)
- H'(−5, 4)

Now, let's compare the original and transformed points:

1. From H(−5, −4) to H'(−5, 4):
- The x-coordinate remains the same (−5).
- The y-coordinate changes from −4 to 4, which is an increase of 8 units.

2. From G(−2, −1) to G'(−2, 1):
- The x-coordinate remains the same (−2).
- The y-coordinate changes from −1 to 1, which is an increase of 2 units.

3. From F(0, −3) to F'(0, 3):
- The x-coordinate remains the same (0).
- The y-coordinate changes from −3 to 3, which is an increase of 6 units.

In all cases, the x-coordinates stay the same, while the y-coordinates are reflected across the x-axis (the negative y-values become positive).

Therefore, the transformation that describes the changes is:

**Reflection across the x-axis.**