Question

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.

Answer 1

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°.