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Question

Find a point on y-axis which is equidistant from the points (5,-2) and (-3,2).


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Solution

Find a point on y-axis which is equidistant from the points (5,-2) and (-3,2):

Let the point be P(0,a) be equidistant from the points A(5,-2) and B(-3,2).

PA=PB.

According to the distance formula, the distance between two points A(x1,y1) and B(x2,y2) is given by:

AB=(x2-x1)2+(y2-y1)2

Let's use the distance formula to substitute the given coordinates in PA=PB:

(5-0)2+(-2-a)2 =(-3-0)2+(2-a)2

(5-0)2+(-2-a)2 =(-3-0)2+(2-a)2 [ squaring both the sides ]

25+4+4a+a2 =9+4-4a+a2

29+4a =13-4a

29-13 =-4a-4a

16 =-8a

a =-2

Hence, (0,-2) is a point on y-axis which is equidistant from the points (5,-2) and (-3,2).


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