Question

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

Answer 1

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)