Minarets are the surrounding towers in a mosque. Mosques have anywhere from one to four minarets (sometimes more).

A pagoda is a type of roof and cannot be the answer. Columns and balusters are not common in Islamic architecture, but these two are not usually independent structures.

Though minarets share the shape of an obelisk, they are not as minimalist in design.

Image is in the public domain, accessed through Wikipedia Media Commons: https://commons.wikimedia.org/wiki/File:Hagia_Sophia_Cathedral.jpg

This is an image of Hagia Sophia in Istanbul, Turkey.

It was first a Greek Basilica church under Constantine and converted to a Mosque when the Turks invaded and occupied Istanbul in 1453.

This is the only answer choice that fits the historical context of being converted to a mosque in this region (Istanbul, Turkey/Greece). Though the Blue Mosque is in Istanbul, it was built after the occupation.

Image is in the public domain, accessed through Wikipedia Media Commons: https://commons.wikimedia.org/wiki/File:Hagia_Sophia_Cathedral.jpg

The influence of Islamic art and architecture can easily be found in Spain, which had Muslim rulers for over 700 years. Thus, the Alhambra and its arabesques is the best choice. Ziggurats predate Islam, pointed arches can't be traced back just to an Islamic influence, and "elaborate designs" is too vague to be correct. 

Coptic art emerged out of Egypt as a product of anti-iconic Christian tendencies. During this period, there was much debate in the emerging Christian church as to whether or not iconography would be permissible in Christian art. The Coptic tradition sided against depictions of the divine, laying the framework for the Islamic style which forbids images of the Prophet as blasphemous. This question challenges students to understand how art history, like history itself, is not a simply defined series of movements, but instead the product of cultural assimilation and synthesis, with complicated politics of power and philosophy that evolve styles and root themselves in meaning and belief.

The Islamification of nearly the entire region created a common theme and mission, namely the construction of mosques. With this came a movement away from idolatry in lieu of the complex lattice work that ornaments many mosques. Thus, across an entire region, we see commonalities created by the recurring theme of Islam, and the aesthetics that accompany it, juxtaposed with the individual traditions upon which the religion was lain. This question tests a student's ability to frame a movement within the larger picture of history, while recognizing how cultural revolutions create both larger communities and individual differences with and between aesthetic traditions.