Question

Find the coordinates of the point on x-axis, which is equidistant from the points (-2,5) and (2,-3).​

Answer 1

Answer:

equidistant from the points (−2,5) and (2,−3)

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ANSWER

Let the point on the x−axis be P(a,0)

Let the other two point be A(−2,5) and B(2,−3)

So by distance formula we have,

Distance between two points = (x2−x1)2+(y2−y1)2

Then,

PA=PB

PA2=PB2

⇒(a+2)2+(0−5)2=(a−2)2+(0+3)2

⇒a2+4+4a+25=a2+4−4a+9

⇒4a+29=−4a+13

⇒ 8a=−16⇒a=−2

∴ The required point isP(−2,0)