A distributed antenna system (DAS) consists of several interconnected access points (APs) which are distributed over an area. Each AP has an antenna array. In previous studies, the DAS has been demonstrated great potential to improve capacity and power efficiency compared to a centralized antenna system (CAS) which has all the antennas located in one place. The existing research also has shown that the placement of the APs is essential for the performance of the DAS. However, most research on AP placement does not take into account realistic constraints. For instance, they assume that APs can be placed at any location in a region or the array radiation pattern of each AP is isotropic. This paper focuses on optimizing the AP placement for the DAS with massive MIMO (D-mMIMO) in order to reduce the transmit power. A square topology for the AP placement is applied, which is reasonable for deploying the D-mMIMO in urban areas while also offering theoretically interesting insights. We investigate the impact of the radiation pattern, signal coherence, and region size on the D-mMIMO's performance. Our results suggest that i) among the three factors, the array radiation pattern of each AP is the most important one in determining the optimal AP placement for the D-mMIMO; ii) the performance of the D-mMIMO is highly impacted by the placement and array radiation pattern of each AP, the D-mMIMO with unoptimized placement may perform even worse than the CAS with massive MIMO (C-mMIMO); iii) with the consideration of patch antennas and the mutual coupling effect, the optimized D-mMIMO can potentially save more than 7 dB transmit power compared to the C-mMIMO. Furthermore, our analytical results also provide an intuition for determining an adequate AP placement for the D-mMIMO in practice.