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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

In the figure shown, O A B C is a rectangle with O A = 3 units, O C = 4 units. If B D = 2.5 units, then the slope of the diagonal O B is equal to

Options

A1 2
B2 3
C1 2
D1 3

Correct answer

C. 1 2

Step-by-step solution

tan ⁡ θ = 3 4 , tan ⁡ ϕ = 3 2 3 = 1 2 slope of O B = tan ⁡ π 2 - θ + ϕ = cot ⁡ θ + ϕ = 1 − 3 4 ⋅ 1 2 3 4 + 1 2 = 1 2

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