Since, the distance between the points (x, y) and (1, 2) is 2 units, then (x−1)2+(y−2)2=4 This is possible only when, Case 1 (x−1)2=0 and (y−2)2=4 ⇒x=1 and y=0,4 So the points are (1, 0), (1, 4) Case II (x−1)2=4 and (y−2)2=0 ⇒x=3,−1 and y=2 So the points are (3,2),(3,–1) Hence, there are total 4 points with integral co-ordinates.