Name a point that is between 50 and 60 units away from (7,-2) and state the distance between the two points.

At first question unclear, that's what I understood is that you wanna  a  point that is far away from other by a distance from 50 to 60 

Let D be the distance between the two points , other Point (x,y)

D = sqrt[ (x-7)^2 + (y+2)^2)   => (1)

the distance is between 50 , 60:

50 < D < 60

From (1);

50 < sqrt((x-7)^2 + (y+2)^2) < 60   

Pick any x : let x = 7

50  < |y+2|< 60     (solve for y)

48 < y < 58

-48 > y > -58

Take any point in the range:

(7, 49) << This point will give you the distance between the two point is in range 50 to 60