This pattern is used when you make a judgment or inference based on something you directly observe or know. It is similar to saying 'judging from the fact that...' or 'seeing that...' in English. The evidence can be something you see, hear, or have learned, but it is usually something concrete and observable, not just a guess.

The pattern is quite natural in both spoken and written Japanese, but it carries a slightly analytical tone, so it is often used in reasoning or explanations. You can use it in casual conversation, but it is more common in formal or semi-formal contexts. Note that the verb before ところを見ると is often in the past tense, but present tense is also possible if you are describing a habitual or ongoing situation.

Be careful with the nuance: the conclusion is based on the evidence you mention, so it is not a strong statement of certainty but rather a reasonable inference. For example, if you see someone sleeping at their desk, you might say that they must have been tired, but you are not 100% sure.