Question

find the point on the x-axis which is equidistant from (2,-5)(-2,9)​

Answer 1

Equidistant point means Midpoint

X1 = 2, X2= -2, Y1= -5, Y2= 9

Therfore by using midpoint formula

x = X1 + X2/2

x = 2-2/

x = 0/2

x = 0

y = Y1 + Y2/2

= -5 + (-2)/2

= -5 -2/2

= 7/2

= 3.5

Therfore the equidistant point is (x, y) (0, 3.5)

Answer 2

Step-by-step explanation:

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

4−4x+x²+25=4+4x+4+81

⇒8x=25−81

⇒8x=−56

⇒x=−7

So, point is (−7,0).