Circle J has center J (4,-3) and radius 5 What is the measure, in degrees, of the arc with endpoints A (9,-3) and B (4,2)? Explain the process you used (in words) and include the work you did to find this answer.

• MsEHolt: This would be a 90° arc.
  
  To find this, we can find the measure of the central angle that intercepts the arc.
  
  The endpoints of the arc are at (9, -3) and (4, 2).
  The slope of the line that passes through the endpoint (9, -3) and the center (4, -3) is given by 
  m=(-3--3)/(9-4) = 0/5 = 0.
  
  Since the slope is 0, this tells us it is a horizontal line.
  
  The line that passes through the endpoint (4, 2) and the center (4, -3) has a slope that is undefined; it is a vertical line at x=4.  Numerically the slope is given by 
  m=(2--3)/(4-4) = 5/0, which is undefined.
  
  These slopes are negative reciprocals of one another; 5/0 and 0/5 (0 has no sign).  This means that these two lines would form a right angle, so the central angle of the circle is a right angle.  
  
  The intercepted arc has a measure equal to that of the central angle, so the arc is also 90°.