Question

if the corderanates of the vertex of two points b is o 3 and c 0 - 3 find cordenate a​

Answer 1

Answer:Let the third vertex of the equilateral ΔABC be A(x,y)

So by distance formula we have,

Distance between two points =  

(x  

2

​

−x  

1

​

)  

2

+(y  

2

​

−y  

1

​

)  

2

 

​

 

∴BC=  

(0−0)  

2

+(3+3)  

2

 

​

=  

6

​

 

2

=  

36

​

=6

∴AB=  

(x−0)  

2

+(y+3)  

2

 

​

 

⇒AB  

2

=x  

2

+y  

2

+2y=27  -----(1)

Now, AC=  

(x−0)  

2

+(y−3)  

2

 

​

 

⇒AC  

2

=x  

2

+y  

2

+9−6y=36

⇒27−2y−6y+9=36

⇒−8y=36−36

⇒y=0

∴x  

2

=27

⇒x=  

27

​

=  

3×3×3

​

=+3  

3

​

or−3  

3

​

 

∴ Required points are A(3  

3

​

,0) and A(−3  

3

​

,0)

Step-by-step explanation: