According to the analysis, the line segment of 1cm on the diagram represents 0.5km, as shown below:

(1) The park is 0.5km south-east of Hongqi Primary School. On the map, it is 0.5÷0.5= 1 (cm).

(2) The library is located at the northwest of Hongqi Primary School 1 km, which is1.5 = 2 (cm) on the map;

(3) The supermarket is located at 50 directions southwest of Hongqi Primary School 1.5km, that is, 50 directions southwest of Hongqi Primary School on the map1.5 ÷ 0.5 = 3 (cm);

(4) The square is located at 30 northeast of Hongqi Primary School 1 km, that is, 30 northeast of Hongqi Primary School on the map1.5 = 2 (cm);

As shown in the figure: