Slope Of A Line

Since the particle gets reflected upon hitting the x-axis, the angle of incidence is equal to the angle of reflection.

(In other words, the angle the particle makes with the x-axis before hitting the x-axis is the same as the angle it makes with the x-axis after reflection.)

The initial position of the particle is and the point where it gets reflected is . The slope of the line connecting these two points is given by:

Hence Slope of the line is

To calculate the variance of the numbers 6, 7, 8, 9, we use the formula for variance: where is the mean of the numbers and is the number of observations.
Step 1: Calculate the mean The numbers are 6, 7, 8, and 9. First, find the mean: Step 2: Calculate the squared differences from the mean Now, we calculate the squared differences from the mean for each number:

Step 3: Find the variance The variance is the average of the squared differences:
Thus, the variance is . Therefore, the correct answer is option (E).