Question

find the point on y axis which is equidistant from (5, - 2) (- 3, 2)

Answer 1

Answer:(0,-2)

Explanation:let the required point be p(a,b).

Given points be A,B respectively.

Since the point lies on y-axis ,then x=0.

Hence,the required point is of the form (0,b).

Then

The given points are equidistant from (0,b).

We know distance formula is √(x1-x2)²+(y1-y2)²

Then,

PA=PB

PA²=PB²[since equidistant]

(0-5)²+(b+2)²=(0+3)²+(b-2)²

25+b²+4+4b=9+b²+4-4b

29+4b=13-4b

16+8b=0

8b=-16

b=-2

Hence the required point is (0,b)=(0,-2).

Answer 2

√2

Explanation:

Let us take point on Y axis as (X,Y)

Suppose A(5,-2) be (X1,Y1)

B(-3,2) be (X2,Y2)

X1=5, Y1=-2, X2= -3,Y2=2.

By distance formula:-

d(A,B)=√(X2-X1)²+(X2-Y1)²

=√(5-(-2))+((-3)-2)

=√(5+2)+(-5)

=√7-5

=√2

I think I am right.