Question 84

What is the slope of the line perpendicular to the line passing through the points (4,5) and (3,2)?

Solution

Slope of line passing through points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ = $$\frac{(y_2 - y_1)}{(x_2 - x_1)}$$

Points = A (3,2) and B (4,5)

=> Slope of AB = $$\frac{5 - 2}{4 - 3} = 3$$

Product of slopes of two perpendicular lines = -1

Let slope of line perpendicular to AB = $$m$$

=> $$m \times 3 = -1$$

=> $$m = \frac{-1}{3}$$

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What is the slope of the line perpendicular to the line passing through the points (­4,5) and (3,­2)?