Question

Find the point on the x− axis which is equidistant from (2,−2) and (−4,2)

Answer 1

Step-by-step explanation:

Let the required point on the X-axis be P(x,0)

As given P is equidistant from A(2,−5) and B(−2,9)

∴PA=PB

⇒

(x−2)

2

+(0−(−5))

2

=

(x+2)

2

+(0−9)

2

⇒(x−2)

2

+25=(x+2)

2

+81

⇒x

2

−4x+4+25=x

2

+4x+4+81

⇒−8x=85−29

⇒−8x=56

⇒x=

−8

56

=−7

∴ Required point on X-axis =(−7,0)