Answer :

Final Answer:

The lines JK and LM are perpendicular. This determination arises from their slopes being negative reciprocals of each other, indicating perpendicularity.

Explanation:

To determine the relationship between lines JK and LM, we'll examine their slopes. Let's denote the slopes of JK and LM as m1 and m2, respectively. The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).

Given the coordinates of J(3, 4) and K(7, -2), the slope of JK (m1) can be calculated as follows: m1 = (-2 - 4) / (7 - 3) = -6 / 4 = -3 / 2.

For the coordinates of L(2, 1) and M(5, -5), the slope of LM (m2) is: m2 = (-5 - 1) / (5 - 2) = -6 / 3 = -2.

Comparing the slopes, m1 = -3/2 and m2 = -2. When two lines are perpendicular, their slopes are negative reciprocals of each other. Here, m1 * m2 = (-3/2) * (-2) = 3, indicating perpendicular lines as their slopes' product is -1.

Hence, the lines JK and LM are perpendicular due to their slopes satisfying the condition for perpendicularity (m1 * m2 = -1). Therefore, the final conclusion is that JK and LM are perpendicular lines.

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Rewritten by : Barada