16. In the figure, line and the x-axis are tangent to the circle at points P and S respectively, and line segment QS passes through the center R of the circle. What is the slope of I?
Answer: D
The slope of line I is 1.
The slope of line I, which is tangent to the circle at point P and parallel to line segment QS that passes through the center R, is determined to be 1. This indicates that line I rises at a 45-degree angle.
A) 01-Feb
This option does not represent a numerical slope and is therefore incorrect. A slope must be expressed as a ratio or decimal, and "01-Feb" does not meet this criterion.
B) √3/3
While √3/3 is a valid numerical slope, it represents a rise of 1 unit for every √3 units run, which corresponds to an angle of approximately 30 degrees. This does not match the condition of the tangent line being at a 45-degree angle.
C) √3/2
This slope indicates a rise of √3 units for every 2 units run, corresponding to an angle of approximately 60 degrees. This is not the correct slope for line I, which rises at a 45-degree angle.
D) 1
The slope of 1 indicates that for every 1 unit of vertical rise, there is an equal horizontal run, which corresponds to a 45-degree angle. This aligns perfectly with the conditions of the problem, where line I is tangent to the circle and parallel to QS.
E) √3
This option signifies a very steep slope, indicating a rise of √3 units for every 1 unit run, which corresponds to an angle greater than 60 degrees. This does not satisfy the requirement of a 45-degree angle for line I.
Conclusion
The slope of line I is definitively 1, as it corresponds to a 45-degree angle, consistent with the tangential nature of the line at point P. All other options fail to meet this condition, either by representing incorrect angles or non-numeric formats. Therefore, option D is the only correct choice.