Final answer:
By calculating the slopes of the lines formed by the point pairs, we can determine that the lines JK and LM are neither parallel nor perpendicular for the first set, perpendicular for the second set, parallel for the third set, and perpendicular for the fourth set, with one line along the x-axis and the other along the y-axis.
Step-by-step explanation:
To determine if the lines formed by the sets of points are parallel, perpendicular, or neither, we need to calculate the slopes of the lines formed by the point pairs JK and LM. If the slopes are equal, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular. If neither condition is met, the lines are neither parallel nor perpendicular.
Calculation of Slopes:
For points J(1, 9) and K(7, 4), the slope is (4 - 9) / (7 - 1) = -5/6.
For points L(8, 13) and M(-2, 1), the slope is (1 - 13) / (-2 - 8) = -12/-10 = 6/5.
For points J(13, -5) and K(2, 6), the slope is (6 - (-5)) / (2 - 13) = 11 / -11 = -1.
For points L(-1, -5) and M(-4, -2), the slope is (-2 - (-5)) / (-4 - (-1)) = 3 / -3 = -1.
For points J(-10, -7) and K(-4, 1), the slope is (1 - (-7)) / (-4 - (-10)) = 8/6 = 4/3.
For points L(-3, 2) and M(-6, -2), the slope is (-2 - 2) / (-6 - (-3)) = -4/-3 = 4/3.
For points J(11, -2) and K(3, -2), the slope is (-2 - (-2)) / (3 - 11) = 0, which is along the x-axis.
For points L(1, -7) and M(1, -2), the slope is undefined as the x-values are the same, indicating a line parallel to the y-axis.
Analysis:
The lines JK and LM for the first set of points are neither parallel nor perpendicular as their slopes are not equal or the negative reciprocal of each other.
The lines JK and LM for the second set of points are perpendicular as their slopes are negative reciprocals of each other (-1).
- The lines JK and LM for the third set of points are parallel as their slopes are equal (4/3).
- The lines JK and LM for the fourth set of points are perpendicular as one line is along the x-axis and the other is along the y-axis.