In the xy plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r= Pick:
A) 6  B) 5  C) 4  D) 3  E) 2
This question might look intimidating because of its language, but once you start solving it, you will realise that the options are given to you in such a way that you reach the correct answer easily.   The radius will lie somewhere between the distance of centre from the inner point and the distance from the outer point.   Distance between centre and inner point = Distance between (-2,-3) and (-2, 1)   We can solve for the distance by using the formula for distance between two points. But that is not required here.   If one of the co-ordinates is same, then the distance between two points is simply the difference between the other coordinate.   In this case, Distance = 1 - (-3)= 
<gadget id="calculator">1 - (-3)</gadget>
<output>4</output>
4   Distance between centre and utter point= Distance between (-2, -3) and (4, -3) = 4 - (-2)= 
<gadget id="calculator">4 - (-2)</gadget>
<output>6</output>
6   The radius has to be between 4 and 6   On looking at the options, only 5 satisfies   Correct Option: 5
<result>B</result>
In the xy plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r=