High School

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Given that line segment \( JK \) has coordinates \( J(-3, 9) \) and \( K(5, -1) \), and line segment \( LM \) is perpendicular to \( JK \), what is the slope of \( LM \)?

Answer :

Final answer:

The slope of LM is 4/5.

Explanation:

To find the slope of LM, we first need to find the slope of JK. The slope of a line is determined using the formula: slope = (y2 - y1) / (x2 - x1). For JK, we have the coordinates J (-3, 9) and K (5, -1). So, the slope of JK is (9 - (-1)) / (-3 - 5) = 10 / -8 = -5/4.

Since LM is perpendicular to JK, the slopes of the two lines are negative reciprocals of each other. Therefore, the slope of LM is the negative reciprocal of -5/4, which is 4/5.

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