Question

P(3.1), Q(6,5) and R(x, y) are three points such that the angle PRQ is a right angle and the area of triangle RPQ=7. Then the number of points of R is ​

Answer 1

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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 △RPQ=7, then the number of such points R is

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Correct option is

A

2

Since the angle RPQ is a right angle,

∴ Slope of RP× Slope of PQ=−1

⇒

3−x

1−y

×

6−3

5−1

=−1⇒3x+4y=13 ...(1)

Also, area of △RPQ=7

⇒

∣

∣

∣

∣

∣

∣

∣

∣

2

1

∣

∣

∣

∣

∣

∣

∣

∣

x

3

6

y

1

5

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

=7

⇒

2

1

[x(1−5)−y(3−6)+1(15−6)]=±7

⇒−4x+3y+9=±14⇒−4x+3y=5 ...(2)

and −4x+3y=−23 ...(3)

Solving (1) and (2) and (1) and (3), we get two different coordinates of point R.

So, there two such points.