Question

Give one pair of value of x and y such that (x,y) is equidistant from the point (-1,8) and (3,4). justify your step​

Answer 1

Step-by-step explanation:

Step -1: Framing Equation pertaining to the conditions given in the Problem.

Let P(x,y) be equidistant from A(−1,8) and B(3,4).

So, PA = PB

(x + 1)

2

+(y−8)

2

=

(x−3)

2

+(y−4)

2

Step -2: Solve the equation formed to find the value of x and y.

(x + 1)

2

+(y−8)

2

=

(x−3)

2

+(y−4)

2

Squaring on both sides,

⇒x

2

+1+2x + y

2

+64−16y = x

2

+9−6x + y

2

+16−8y

⇒2x−16y + 65 = −6x−8y + 25

⇒8x−8y = −40

⇒x−y = −5

All the points lying on line will be equidistant from (−1,8) and (3,4).

So, y = 6 and x = 1.

Hence, the P(x,y) is (1,6).