Question

Give one pair of values of x and y such that (x, y) is equidistant from the points
(-1,8) and (3, 4). Justify your steps.​

Answer 1

Answer:

(1 ,6)

Step-by-step explanation:

A ( -1,8)    B(3,4)

mid point of AB  =  (-1+3) /2   ,  (8+4) /2

                          =   (1 ,6)

C (x,y)  =  (1,6)

using distance formula

AC =   BC  = √8

Answer 2

Let A(-1,8) be (x1,y1)

B(3,4) be (x2,y2)

& P(?,?) be (x,y)

If we draw this information on co-ordinate system the pt. P will lie on Y-axis. Therefore, it's x-cordinate will be '0'.

Now,

d(P,A) = d(P,B)

Squaring both sides,

PA^ = PB^

[By distance formula]

(x-x1)^+(y-y1)^ = (x-x2)^+(y-y2)^

(0+1)^+(y-8)^ = (0-3)^+(y-4)^

0+y^-16y+64 = 0+y^-8y+16

-16y+64 = -8y+16

-16y+8y = 16-64

-8y = -48

Therefore,y=6

Result : (x,y) = (0,6)

I think this will help you;

& If this is wrong you can say me in comment box , Thanks.