Given: The distance between the points (5, - 2) and (1, a) is 5. Let A = (5, - 2) and B = (1, a) As we know that, the distance between the points A and B is given by: |AB|=√(x2−x1)2+(y2−y1)2 Here, x1=5,y1=−2,x2=1 and y2=a ⇒AB|=√(1−5)2+(a+2)2=5 By squaring both the sides of the equation we get, ⇒25=16+(a+2)2 ⇒9=(a+2)2⇒(a+2)=±3 Case 1: When (a+2)=3 then a=1 Case 2: When (a+2)=−3 then a=−5 Hence, a=1,−5