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 A RPQ=7. Then the number of points of R is..?​

Answer 1

Answer:

Step-by-step explanation: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.