Write a rule to describe each transformation.

Question

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.