Question

Find the point on y- axis which is equidistant from the points (5, -2) and (-3, 2).
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Answer 1

=> Let P(m,n) be point on y- axis which is equidistant from the points (5, -2) and (-3, 2).

Now, m = 0 [ because P(m,n) lies on y - axis ]

=> Now, we will find out distance between P(0,n) and (5,-2) :-

Let d be distance between P(0,n) and (5,-2) :-

=> d² = (0-5)² + ( n+2)²

=> d² = 25 + ( n+2)².......... (1)

=> Now, we will find out distance between P(0,n) and (-3, 2) :-

Let t be distance between P(0,n) and (-3, 2) :-

=> t² = (0+3)² + ( n-2)²

=> t² = 9 + ( n-2)²......(2)

=> Distance between P(0,n) and (5,-2) = Distance between P(0,n) and (-3, 2)

=> d = t

=> d² = t²

From equation (1) and (2) :-

=>25 + ( n+2)² = 9 + ( n-2)²

=>25 + n²+4 +4n = 9 + n²+4 - 4n

=>25 + n²+4 +4n - (9 + n²+4 - 4n) = 0

=>25 + n²+4 +4n - 9 -n²-4 + 4n = 0

=>25- 9 + 8n = 0

=>16 + 8n = 0

=> 8n = -16

=> n = -16/8

=> n = -2

=> P(m,n) = P(0,-2)

Answer :

The point on y- axis which is equidistant from the points (5, -2) and (-3, 2) = (0,-2)