Question

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

Explanation:

Step1: Analyze Reflection

First, check reflection across y - axis. A reflection across the y - axis changes the x - coordinate of a point \((x,y)\) to \((-x,y)\). For the left figure (JKLMN) and the right figure (VWXYZ), reflecting JKLMN across the y - axis would mirror it.

Step2: Analyze Translation

After reflection, we need to check the translation. Let's take a key point, say point J in JKLMN. The coordinates of J (approximate) before reflection: let's assume J is at \((-5,-6)\). After reflection across y - axis, it becomes \((5,-6)\). Now, the corresponding point W in VWXYZ is at \((4,-6)\)? Wait, no, let's re - check. Wait, maybe a better point: the vertex of the "V" shape, M in JKLMN and Y in VWXYZ. M is at \((-4,-4)\), after reflection across y - axis, it becomes \((4,-4)\). Then, Y is at \((5,-4)\)? Wait, no, maybe I made a mistake. Wait, looking at the graph, after reflecting JKLMN across the y - axis, and then translating 1 unit to the right. Let's check the position of the leftmost point of JKLMN: N is at \((-5,-2)\), after reflection across y - axis, it is \((5,-2)\), then translating 1 unit right? No, wait, the right figure's leftmost point X is at \((4,-3)\)? Wait, maybe a better approach: the two figures are mirror images across the y - axis (reflection) and then shifted 1 unit right. Let's check option B: reflect across y - axis (which flips the figure horizontally) and then translate 1 unit right. This would map JKLMN to VWXYZ. Option A: translating 10 units right would not match the horizontal flip. Option C: translating left would move it in the wrong direction. Option D: they are congruent as they are reflections and translations (rigid transformations) which preserve congruence. So the correct option is B.

Answer:

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