Final answer:
The length of the line segment connecting P (-4, 1) and R (-4, -3) is 4 units, and the segment crosses the third and fourth quadrants as both points have a negative x-coordinate.
Step-by-step explanation:
The question asks for the length of the line segment connecting two points, as well as the quadrant(s) where the segment is located. The two points given are P = (-4, 1) and R = (-4, -3). To find the length of the segment, we can use the distance formula, which is derived from the Pythagorean theorem:
d = √((x2 - x1)2 + (y2 - y1)2)
In this case, since the x-coordinates are the same, the length of the segment is simply the difference in the y-coordinates:
d = √((1 - (-3))2) = √(16) = 4 units
The segment is found within the third and fourth quadrants because both points have a negative x-coordinate.