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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

If the line segment joining P 2,3 and Q 5,7 subtends a right angle at R x , y and the area of Δ P Q R = 2 sq. units, then the maximum number of such points R in xy - plane are

Correct answer

4

Step-by-step solution

P Q = 3 2 + 4 2 = 5 Let, length of altitude through R is h then 1 2 × h × 5 = 2 ⇒ h = 4 5 Maximum possible length of altitude through R with right angle at R of Δ P Q R (without the given area) is equal to 1 2 P Q = 5 2 Now, 4 5 < 5 2 So, 4 triangles are possible

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