Question

Find the coordinates of the point on the xx-axis that is equidistant from (−9,14)-9,14 and (−8,−1)-8,-1.​

Answer 1

Answer:

Since point on x−axis, then coordinate of the point is (x,0).

According to the question this point (x,0) is equidistant from the points (2,−5) and (−2,9).

That is, distance from (x,0) and (2,−5) = distance from (x,0) and (−2,9).

(2−x)

2

+(−5−0)

2

=

(−2−x)

2

+(9−0)

2

⇒(2−x)

2

+(−5)

2

=(−2−x)

2

+(9)

2

⇒4−4x+x

2

+25=4+4x+4+81

⇒8x=25−81

⇒8x=−56

⇒x=−7

So, point is (−7,0).