Why is HttpClient BaseAddress not working?

Consider the following code, where the BaseAddress defines a partial URI path.

using (var handler = new HttpClientHandler())
using (var client = new HttpClient(handler))
{
    client.BaseAddress = new Uri("http://something.com/api");
    var response = await client.GetAsync("/resource/7");
}

I expect this to perform a GET request to http://something.com/api/resource/7. But it doesn’t.

After some searching, I find this question and answer: HttpClient with BaseAddress. The suggestion is to place / on the end of the BaseAddress.

using (var handler = new HttpClientHandler())
using (var client = new HttpClient(handler))
{
    client.BaseAddress = new Uri("http://something.com/api/");
    var response = await client.GetAsync("/resource/7");
}

It still doesn’t work. Here’s the documentation: HttpClient.BaseAddress What’s going on here?