Question

in which situation is the principle of cross - cutting relationships useful in determining relative age?
a fault breaks through sedimentary layers.
fossils of two different species are found in different rock layers.
sedimentary layers form over millions of years in a lake bottom.
lava flows form on top of one another from several eruptions over time.

Explanation:

The principle of cross - cutting relationships states that a geological feature (such as a fault or intrusion) that cuts through another feature is younger than the feature it cuts. In the case of a fault breaking through sedimentary layers, we can use this principle. The fault is the cross - cutting feature. The sedimentary layers were there first (older), and then the fault (younger) broke through them.
For the option with fossils in different rock layers, it is more about the principle of fossil succession. When sedimentary layers form in a lake bottom (over time), it is related to the principle of superposition (lower layers are older). Lava flows on top of one another also relate to superposition (lower lava flow is older).

Answer:

A. A fault breaks through sedimentary layers.