Matthew 2:6-10
Mat 2:6 (KJB)
And thou Bethlehem, in the land of Juda, art not the least among the princes of Juda: for out of thee shall come a Governor, that shall rule my people Israel.
Immediately they gave the king the answer, that it would be in Bethlehem according to the prophet Micah. (Micah 5:2 KJV) But thou, Bethlehem Ephratah, though thou be little among the thousands of Judah, yet out of thee shall he come forth unto me that is to be ruler in Israel; whose goings forth have been from of old, from everlasting. Then there is also a little bit taken from 2 Samuel 5:2. (2 Sam 5:2 KJV) Also in time past, when Saul was king over us, thou wast he that leddest out and broughtest in Israel: and the LORD said to thee, Thou shalt feed my people Israel, and thou shalt be a captain over Israel. Bethlehem was located about 5 miles (8 km) south f Jerusalem. Micah was the only prophet who specifically foretold that the Messiah would be born in Bethlehem.
Mat 2:7 (KJB)
Then Herod, when he had privily called the wise men, inquired of them diligently what time the star appeared.
Herod had accepted the birthplace of the King because he received the answer right from the prophets plus he got the answer from the Sanhedrin which confirmed the prophecy. He also did not question the reliability of the wise men knowing that they would not have followed a star if it meant nothing. Herod knew something was happening right under his authority. He then called in the wise men in a private session and received from them the accuracy of the time when the star had appeared. No doubt Herod had called the wise men privately because his evil mind was already working on how he could destroy the child once he found out where he was born.
Mat 2:8 (KJB)
And he sent them to Bethlehem, and said, Go and search diligently for the young child; and when ye have found him, bring me word again, that I may come and worship him also.
Deception and murder meant nothing to Herod if it would help him to keep his throne. He then dispatches the wise men to Bethlehem which would have been a very short trip and tells them to find the location of the child and get word back to him, so he could worship the child also. Of course, Herod did not have worship on his mind but murder because here was a serious threat to his throne and power. He had his wife and two sons murdered, so he was not above having all the children in Judaea killed to protect his throne.
Mat 2:9 (KJB)
When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was.
As soon as they heard the orders from the king, they had went thinking at that point that Herod was being truthful with them and also wanted to pay homage to the boy king. Now the star which guided them from their homes was now going before them to guide them where the Lord Jesus was. God had continued to guide them to their final destination in finding the home of the Lord Jesus. It guided them to the exact spot where the house of the Lord Jesus was.
Mat 2:10 (KJB)
When they saw the star, they rejoiced with exceeding great joy.
The wise men had rejoiced and not just a smile but they were rejoicing from deep within themselves because they saw the star and knew their journey was almost over and they would soon find the boy king.