An analog clock shows exactly 5 o'clock. If you look at this clock in a vertical mirror, what time will the mirror image appear to show?

Introduction / Context:
Mirror-image clock questions test your spatial reasoning and understanding of how an analog clock looks when reflected in a vertical mirror. When a clock showing a given time is placed in front of a mirror, the reflected image shows a different time that can be computed using a simple rule. Here, the clock shows exactly 5 o'clock, and you must determine what time appears in the mirror image.

Given Data / Assumptions:

• The clock is an analog 12-hour clock with hour and minute hands.

• The actual time on the clock is exactly 5:00 (5 o'clock sharp).

• The mirror is vertical, so we see a left-right reversed image.

• At 5:00, the minute hand points to 12, and the hour hand points to 5.

Concept / Approach:
The standard approach for mirror-image clock problems is to use the idea that a full hour scale from 12:00 to 12:00 is symmetric around 6 o'clock. For times not exactly at 6:00, the mirror-image time can generally be found by subtracting the given time from 11:60 (or 12:00 with an adjustment). The basic rule is: Mirror time = 11 hours 60 minutes − actual time (when expressed in hours and minutes). This gives the reflected time as seen in the mirror.

Step-by-Step Solution:
Step 1: Express the actual time 5:00 in hours and minutes. Step 2: Actual time = 5 hours 00 minutes. Step 3: Use the mirror-time formula: Mirror time = 11 hours 60 minutes − actual time. Step 4: Compute: 11:60 − 5:00 = (11 − 5) hours and (60 − 0) minutes = 6 hours 60 minutes. Step 5: 6 hours 60 minutes is equivalent to 7 hours 00 minutes. Step 6: Therefore, the mirror image of a clock showing exactly 5:00 appears to show 7:00.

Verification / Alternative check:
You can also reason visually: at 5:00, the hour hand points to the 5 on the right side of the clock. In a mirror, positions on the right become positions on the left. The 5 on the right side corresponds to the 7 on the left side (symmetrically placed around the vertical line passing through 12 and 6). The minute hand at 12 remains at the top in the mirror image. So the reflected time shows the hour hand at 7 and the minute hand at 12, which is 7:00.

Why Other Options Are Wrong:
• 12:00: At 12:00, both hands are at the top. This is not the mirror image of 5:00, where the hour hand is not at 12.
• 5:00: This would be the original time, not the mirrored time. A mirror changes the positions of the numbers on the dial left to right.
• 6:00: At 6:00, both hands are vertically aligned (hour at 6, minute at 12), which does not match the mirror reflection of 5:00. It is a symmetric time but not the correct reflection of 5:00.

Common Pitfalls:
Many students assume the time remains the same in a mirror or confuse the rule by subtracting from 12:00 instead of 11:60, which can lead to errors in cases involving exact hours. Others misread the mirrored positions of numbers on the dial. Remember that the mirror reverses left and right, and using the formula Mirror time = 11:60 − actual time is a reliable way to obtain the correct mirrored time.

Final Answer:
The mirror image of a clock that shows exactly 5 o'clock will appear to show 7:00.