Question

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

Answer 1

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Answer 2

We know that a point on the y-axis is of the form (0,y). So,let P(0,y) be the point on y-axis equidistant from the given points A(-5,-2) and B(3,2).

Since P is equidistant from A and B,

AP=BP

⇒√(0+5)²+(y+2)²=√(0-3)²+(y-2)² (Using Distance Formula)

⇒√(25+y²+4y+4)=√(9+y²-4y+4)

⇒√(y²+4y+29)=√(y²-4y+13)

⇒y²+4y+29=y²-4y+13

⇒4y+29=13-4y

⇒8y=16

⇒y=2

Thus, (0,2) is the required point.