To analyze the given scenario of adding a third slit and determining the interference patterns at points $Z$, $Y$, and $X$, let's proceed step by step:

1. Basic Setup:

   • Initially, with two slits, the interference pattern is determined by constructive and destructive interference between light waves originating from the two slits.
   • When a third slit is added, positioned equidistantly between the original two, the distances between slits become halved.

2. Interference Condition:

   • Constructive interference occurs when the path difference between light waves from the slits equals $m\lambda$ (where $m$ is an integer).
   • Destructive interference occurs when the path difference equals $(m + \frac{1}{2})\lambda$.

3. Impact of Adding a Third Slit:

   • With three slits, the contributions from all three need to be summed. The new spacing (half of the original distance) alters the relative phase differences.
   • At points previously associated with constructive interference for two slits, additional interference from the third slit can cause either reinforcement (stronger maxima) or suppression (partial or complete cancellation).

4. Evaluating Points $Z$, $Y$, and $X$:

   • Point $Z$: With three equidistant slits, all contributions can interfere constructively here if the path differences align as multiples of $\lambda$. Thus, $Z$ is likely a point of maximum constructive interference.
   • Point $Y$: At this location, the phases might cancel out (due to the new phase relationships with the third slit). This could result in complete destructive interference if the amplitudes cancel exactly.
   • Point $X$: Similar to $Y$, depending on the phase relationship, interference could lead to a weaker maximum or a point of neither constructive nor destructive interference.

5. Conclusion:

   • The addition of a third slit redistributes the intensity of the interference pattern, with potential new maxima and minima. The final classification depends on detailed calculations of path differences.

If you'd like, I can calculate the exact phase differences and intensities for each point. Let me know!