Geotagged photos have been applied by many researchers to explore the spatial extent of places. This paper addresses an important challenge of using geotagged Flickr photos to delineate the spatial extent of a vague place, which is defined as a place without a clearly defined boundary. We argue that the variation of location popularity has a great impact on the estimation of such vague spatial extent of a place. We propose an approach to model the representativeness of each geotagged photo point based on its location popularity. A modified kernel density estimation method incorporating the photo representativeness is developed and tested with eight places, which cover urban vs. non-urban areas, with vs. without an official boundary cases, and at various spatial scales of state, city and district levels. Our results indicate major improvements of the proposed representativeness-weighted kernel density estimation method over the traditional kernel density estimation method in estimating the spatial extent of vague places.