Question

which statement why figure jkl mn is congruent to figure vwxyz?
a. figure jkl mn was translated 10 units to the right.
b. figure jkl mn was reflected across the y - axis and translated 1 unit to the left.
c. figure jkl mn was reflected across the y - axis and translated 1 unit to the right.
d. figure jkl mn and figure vwxyz are not congruent.

Explanation:

Step1: Analyze Option A

Translation only moves the figure. If we assume translation 10 units right, check the positions. But reflection is also involved (by observing orientation change), so A is wrong.

Step2: Analyze Option B

Reflection across \(y -\)axis changes the \(x -\)coordinate sign. Translating 1 unit left would not align. Incorrect.

Step3: Analyze Option C

Reflect figure \(JKLMN\) across the \(y -\)axis (changes \(x\) - coordinates: \((x,y)\to(-x,y)\)). Then translate 1 unit to the right (\((x,y)\to(x + 1,y)\)). This will map \(JKLMN\) to \(VWXYZ\) as congruent figures (reflection and translation are rigid motions, preserve shape and size).

Step4: Analyze Option D

Since rigid motions (reflection + translation) can map \(JKLMN\) to \(VWXYZ\), they are congruent. So D is wrong.

Answer:

C. Figure \(JKLMN\) was reflected across the \(y -\)axis and translated 1 unit to the right.