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Q.

If two opposite vertices of a square are (5,4) and (1, -6), then find the coordinates of its remaining two vertices.


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a

(8,3) and (2,1)  

b

(8,3) and (2,1)  

c

(8,3) and (2,1)  

d

(8,3) and (2,1)   

answer is A.

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Detailed Solution

It is given that,
Opposite vertices of a square are (5,4) and (1, -6).
Question ImageLet, A=(5,4)andC=(1,6)  .
Since ABCD is a square,
AB=BC=CD=DA  .
Suppose, the coordinate of B is (x, y).
We know that, the distance between any two points in a Cartesian plane M(a,b) and  N(c,d) is given by MN= (ca) 2 + (db) 2  .
Then,
   AC= (15) 2 + (46) 2 = (4) 2 + (10) 2 = 16+100 = 116   Since,
AB=BC=CD=DA= AC 2 AB=BC=CD=DA= 116 2 AB=BC=CD=DA= 58  
Now,
AB=BC  
(x5) 2 + (y4) 2 = (1x) 2 + (y(6)) 2  
x 2 10x+25+ y 2 8y+16=12x+ x 2 + y 2 +12y+36  
8x+20y=4  
y= 12x 5      … (1)
In ABC,
B=90° Then by using Pythagoras Theorem we get,
Question Image Therefore,
B 8,3 andD 2,1 .  
Hence, option (1) is correct.
 
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