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 congruence and transformations

Congruent figures have same shape/size, preserved by reflections/translations. Check each option:

• Option B: Says they're not congruent (wrong, congruent via transformations).
• Option C: Translation 10 right? Check coordinates (e.g., J: (-6, -6); W: (-6, 4). Y-axis reflection: J→(6, -6), then translate 1 right? No, C's translation is wrong.
• Option D: Reflect across y-axis (J→(6, -6)) then translate left? Contradicts W's y-coordinate (4).
• Option A: Reflect JKL MN across y-axis (x flips sign: J(-6,-6)→(6,-6)), then translate 1 right: (6+1, -6)=(7,-6)? Wait, maybe better: W is at (-6,4)? Wait, no, looking at graph: J is at (-6, -6) (wait, y-axis: maybe I mixed x/y. Wait, standard graph: x-axis horizontal, y vertical. So J: let's see, green figure JKL MN: J is at (x=-6, y=-6)? Wait, no, the grid: x-axis (horizontal) with positive right, y-axis (vertical) positive up. Wait, the lower green figure VWXYZ: W is at (x=-6, y=4)? Wait, maybe I misread. Wait, the top green: J at (-6, -6)? No, maybe y-axis is reversed. Wait, the key: reflection over y-axis (flips x-coordinate sign) and translation. Let's check option A: "reflected across y-axis and translated 1 unit right". Let's take a point: J (top figure) to W (bottom figure). Suppose J is (x1, y1), W is (x2, y2). After y-axis reflection, x becomes -x1, then translate 1 right: -x1 +1 = x2. Let's assume J is (-6, -6), W is (-6, 4)? No, maybe y-coordinate: top figure is in lower y (negative), bottom in positive. Wait, maybe reflection over x-axis? No, option A is y-axis. Wait, maybe the correct transformation is reflection over y-axis (flips left-right) and translation. Option A says that, and since reflection and translation preserve congruence, this explains why they're congruent. Other options: B is wrong (they are congruent), C's translation is 10 right (too much), D's translation left (wrong direction). So A is correct.

Answer:

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