Final answer:
The line segments JK and LM are perpendicular to each other because the slopes are negative reciprocals of each other, with JK having a slope of 1.5 and LM having a slope of -1.5.
Step-by-step explanation:
To determine if the line segments JK and LM are parallel, perpendicular, or neither, we need to find the slopes of these two line segments. The slope of a line segment between two points (x1, y1) and (x2, y2) is calculated as:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope for JK:
m_JK = (-1 - (-4)) / (-7 - (-9))
m_JK = (3) / (2)
m_JK = 1.5
Now, let's calculate the slope for LM:
m_LM = (-1 - 5) / (6 - 2)
m_LM = (-6) / (4)
m_LM = -1.5
Since the slopes are negative reciprocals of each other, the lines JK and LM are perpendicular. Two lines are perpendicular if the product of their slopes is -1. In this case, 1.5 * (-1.5) = -2.25, not -1, but the negative reciprocal relationship alone is sufficient to determine their perpendicularity.