Question

a point equisdant from the point (0,0) (2,0) (0, 2)​

Answer 1

Step-by-step explanation:

• Let P(x,y) is equidistant from the points A(0,0),B(2,0) and C(0,2). 
• So. PA=PB=PC
• Using the distance formula we get,
• PA=x2+y2
• PB=(x−2)2+y2
• PC=x2+(y−2)2
• ∵PA=PB
• Squaring both sides. ⇒PA2=PB2
• ⇒x2+y2=(x−2)2+y2
• ⇒x2=x2+4−4x
• ⇒4x=4
• ⇒x=1
• Again PA=PC
• Squaring both sides. ⇒PA2=PC2
• ⇒x2+y2=x2+(y−2)2
• ⇒y

Answer 2

Answer:(1,1)

Step-by-step explanation:Let P(x,y) is equidistant from the points A(0,0),B(2,0) and C(0,2).

So. PA=PB=PC

Using the distance formula we get,

PA=

x

2

+y

2

​

PB=

(x−2)

2

+y

2

​

PC=

x

2

+(y−2)

2

​

∵PA=PB

Squaring both sides. ⇒PA

2

=PB

2

⇒x

2

+y

2

=(x−2)

2

+y

2

⇒x

2

=x

2

+4−4x

⇒4x=4

⇒x=1

Again PA=PC

Squaring both sides. ⇒PA

2

=PC

2

⇒x

2

+y

2

=x

2

+(y−2)

2

⇒y

2

=y

2

+4−4y

⇒4y=4

⇒y=1

Here, required point is (1,1)

Hence, correct choice is (D)