Question

If point (x,y) is equidistant from the points (a+b,b-a) and (a-b,a+b) then prove bx = ay​

Answer 1

Answer:

Step-by-step explanation:

Given-

(x,y);(a+b,b-a) and (a-b,a+b)

Here, x1=a+b ; x2=a-b ; y1=b-a ; y2=a+b ; x=x and y=y

now,

By using mid-point formula:-

x=x1+x2/2 and y=y1+y2/2

x=a+b+a-b/2 and y=b-a+a+b/2

x=2a/2 and y=2b/2

x=a*1                                                        

x/a=1                                                          eq.1

and y=b*1                                                  

y/b=1                                                         eq.2

from eq.1 and eq.2, we get

x/a=y/b

by cross-multiplication

bx=ay

Hence Proved