P(3, 1), Q (6, 5) and R (x, y) are three points such that the angle RPQ is a right angle and the area of ΔRQP = 7, then the number of such points R is

Question

P(3, 1), Q (6, 5) and R (x, y) are three points such that the angle RPQ is a right angle and the area of ΔRQP = 7, then the number of such points R is (A) 0 (B) 1 (C) 2 (D) 4

Tardigrade Admin · Accepted Answer

Since angle RPQ = (π/2), therefore Slope of RP × slope of PQ = -1 ⇒ (y-1/x-3) ×(5-1/6-3) = - 1 ⇒ 3x +4y =13 ...(i) Also, area of Δ RPQ = 7 ⇒ |x&y&1 3 &1&1 6&5&1| = ±7 ⇒ 3y - 4x = 5 or 3y - 4x = -23 ...(ii) Solving (i) and (ii), we get two points .

Q. P(3, 1), Q (6, 5) and R (x, y) are three points such that the angle RPQ is a right angle and the area of ΔRQP = 7, then the number of such points R is

0

1

2

4

Since ∠RPQ=2π​, therefore Slope of RP × slope of PQ = -1 ⇒x−3y−1​×6−35−1​=−1⇒3x+4y=13 ...(i) Also, area of ΔRPQ=7⇒∣∣​x36​y15​111​∣∣​=±7 ⇒3y−4x=5or3y−4x=−23 ...(ii) Solving (i) and (ii), we get two points .

Q. P(3, 1), Q (6, 5) and R (x, y) are three points such that the angle RPQ is a right angle and the area of $Δ$ RQP = 7, then the number of such points R is