The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.
According to analytical geometry, two lines are perpendicular to each other if the product of their slopes are equal to - 1. Slopes can be determine by secant line formula:
m₁ = (5 - 8) / [- 2 - (- 6)]
m₁ = - 3 / 4
m₂ = [(k - 2) - (- 20)] / [13 - (k + 3)]
m₂ = (k + 18) / (10 - k)
(- 3 / 4) · [(k + 18) / (10 - k)] = - 1
(- 3 / 4) · (k + 18) = - (10 - k)
- 3 · (k + 18) = - 4 · (10 - k)
- 3 · k - 54 = - 40 + 4 · k
7 · k = - 54 + 40
7 · k = - 14
k = - 2
The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.
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