Question

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

Explanation:

Step1: Analyze Reflection Across y - axis

Reflection across the y - axis changes the sign of the x - coordinate of a point \((x,y)\) to \((-x,y)\). For the figure J K L M N, reflecting across the y - axis will flip it over the y - axis.

Step2: Analyze Translation

Translation is a rigid transformation that moves a figure without changing its shape or size. A translation of 1 unit to the right changes the x - coordinate of a point \((x,y)\) to \((x + 1,y)\).

Step3: Check Congruence

Rigid transformations (reflection and translation are both rigid transformations) preserve the shape and size of a figure, so the image after a rigid transformation is congruent to the original figure. Option A describes a reflection across the y - axis and a translation 1 unit to the right, which are rigid transformations, so it explains why the figures are congruent. Option B says they are not congruent, which is wrong. Option C: translation 10 units to the right does not match the visual (from the graph, the translation seems to be 1 unit). Option D: reflection across y - axis and translation 1 unit to the left would not map J K L M N to V W X Y Z.

Answer:

A. Figure JKLMN was reflected across the y - axis and translated 1 unit to the right.