Question

which statement explains why figure jklmn is congruent to figure vwxyz?

figure jklmn was reflected across the y-axis and translated 1 unit to the left.

figure jklmn and figure vwxyz are not congruent.

figure jklmn was translated 10 units to the right.

figure jklmn was reflected across the y-axis and translated 1 unit to the right.

Explanation:

Identify coordinates of the figures

Using the Geometric Transformations knowledge point

$$
LATEXBLOCK0
$$

Analyze the transformation mapping

Using the Geometric Transformations knowledge point

$$
LATEXBLOCK1
$$

Test reflection across the y-axis

Using the Geometric Transformations knowledge point

$$ (x, y) ightarrow (-x, y) $$

$$
LATEXBLOCK2
$$

Determine the translation vector

Using the Geometric Transformations knowledge point

$$
LATEXBLOCK3
$$

Since the translation vectors do not match, a simple reflection across the \(y\)-axis followed by a translation does not map \(JKLMN\) to \(VWXYZ\).

Test direct translation

Using the Geometric Transformations knowledge point

$$
LATEXBLOCK4
$$

Since the horizontal shifts are not equal, a pure translation does not map the figures. Thus, the figures are not congruent because no single rigid motion or standard composition of these transformations maps \(JKLMN\) directly onto \(VWXYZ\).

Answer:

• Figure JKLMN was reflected across the y-axis and translated 1 unit to the left.
• Figure JKLMN and figure VWXYZ are not congruent. (Correct answer)
• Figure JKLMN was translated 10 units to the right.
• Figure JKLMN was reflected across the y-axis and translated 1 unit to the right.