Question

The point on the y-axis which is equidistant from (2 , -5 ) and (-2 , 9 ) is 

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Answer 1

Step-by-step explanation:

So,the point (0, y) is equidistant from (- 5, 2) and (9, -2).

Since their distance is equal we can apply the distance formula.

Applying distance formula,

d = √[(x2 − x1)2+(y2 − y1)2]

= √[{0 - (- 5)}2 + (y - 2)2] = √[(9 - 0)2 + ( -2 - y)2]

Now simplifying step by step to find the value of y.Now simplifying step by step to find the value of y.

25 + y2 + 4 - 4y = 81 + 4 + y2 + 4y

29 - 4y = 85 + 4y

8y = -56

y = -56 / 8 = -7

The value of y is -7.

Hence, the point on the y-axis that is equidistant from (- 5, 2) and (9, -2) is (0,-7).