P (5, -1) and Q (5, 10) lie on a straight line.The following are a few statements concerning these points on the line.

To analyze the points P(5, -1) and Q(5, 10) and their implications on the straight line, let's break down the statements you may have concerning these points:

1. Vertical Line

Both points have the same x-coordinate (5), indicating that the line is vertical. The equation of a vertical line is of the form $x = a$, where $a$ is the constant x-value. In this case, the equation of the line containing the points P and Q is:

$x = 5$

2. Slope of the Line

In a vertical line, the slope is undefined. This can be understood because the slope is calculated as the change in y over the change in x. Since the x-coordinates are the same (5), the denominator in the slope formula becomes zero, leading to an undefined slope. This results from the formula for slope $m$:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - (-1)}{5 - 5} = \frac{11}{0}$

3. Distance Between Points

To find the distance $d$ between points P and Q, which lie on the same vertical line, we can use the distance formula:

$d = |y_2 - y_1| = |10 - (-1)| = |10 + 1| = 11$

Summary of Findings:

• The line is vertical with the equation $x = 5$.
• The slope of this line is undefined.
• The distance between the points P and Q is 11 units.

This information clarifies the characteristics of the straight line described by points P and Q. If you have specific statements to analyze, please provide them for a more detailed examination!