State whether the following statement is true or false.The points (20,3),(19,8) and (2,-9) are all equidistant from the point

(7,3)
.

Question

State whether the following statement is true or false.The points (20,3),(19,8) and (2,-9) are all equidistant from the point

(7,3)
  .

Accepted Answer

Given points,20,3,19,8, 2,-9, and (7,3) .Let,

A(20,3), B(19,8), C(2,−9), and, O(7,3).
  Since,The distance between any two points in a Cartesian plane

M
    
     a,b
   ,N
    
     c,d
   
   is given by

MN=

(c−a)
      2
     
     +
      
       (d−b)
      2

.Then,

AO=

(20−7)
        2
       
       +
        
         (3−3)
        2

⇒AO=

13
        2
       
       +
        0
        2

⇒AO=13                      ...(1)

BO=

(19−7)
            2
           
           +
            
             (8−3)
            2

⇒BO=

12
            2
           
           +
            5
            2

⇒BO=
          
           144+25

⇒BO=
          
           169

⇒BO=13                     …(2)

And

CO=

(2−7)
        2
       
       +
        
         (−9−3)
        2

⇒CO=

(−5)
        2
       
       +
        
         (−12)
        2

⇒CO=
      
       25+144

⇒CO=
      
       169

⇒CO=13         ...(3)

Then, from (1),(2) and (3),

AO=BO=CO=13.

So, points

(20,3),(19,8)
   and

(2,−9)
   are all equidistant from

(7,3)
  .Therefore, given statement is true.Hence, option (1) is correct.

State whether the following statement is true or false.

The points $(20, 3), (19, 8) and (2, - 9)$ are all equidistant from the point $(7, 3)$ .

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State whether the following statement is true or false.The points (20,3),(19,8) and (2,-9) are all equidistant from the point (7,3) .