Because grammar, "بلد" is the mubtada' in this nominal sentence (subject).. And "ك" is the attached pronoun with kasra for female and fatHa for male. In another case like ".. في بلدِكَ.." (.. in your country.. ) we use kasra on dal because the name was following a kind of propositions.. Another case " أَتُحِبُ بَلَدَك؟" (do you love your country?) we use fatHa on dal because the name is the object in a verbal sentence. The last letter of a word is important for grammar, but pay attention to attached pronouns, they are not not the original last letter. بلد is a name. ك is added and it's removable.
بلدُكَ : if you talk to a male بلدُكِ:if you talk to a female Both means Your country
A ِ should be at the end under the ك to be understood and pronounced as a female not male
بلدُكِ it should be Please don't teach wrong grammar. Stick to MSA or dialect. Don't try to mix them. It's only going to confuse beginners.
"Where is your country?" I guess the scenario is them looking at a map. Other than that it'd be really weird!