Final answer:
To find the value of k, we need to determine the slopes of two lines and set them as negative reciprocals since the lines are perpendicular. By solving the equation, k is found to be -18.
Step-by-step explanation:
To find the value of k, we need to determine the slope of the line joining the points (-5, k) and (3, 10), and then find the negative reciprocal slope of the line joining the points (1, 2) and (-2, 5). Let's calculate:
The slope of the line connecting (-5, k) and (3, 10) is given by: m = (10 - k) / (3 - (-5)) = (10 - k) / 8.
The slope of the line connecting (1, 2) and (-2, 5) is given by: m' = (5 - 2) / (-2 - 1) = 3 / (-3) = -1.
Since the lines are perpendicular, the product of their slopes should be equal to -1. Therefore, (-1) = (10 - k) / 8.
By solving this equation, we find that k = -18.
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