Question

Which point on y-axis is equidistant from (2, 3) and (-4, 1)?

Answer 1

The distance d between two points (x₁, y₁) and (x₂,y₂) is given by the formula:

d=√(x₁ - x₂)² + ( y₁ - y₂)²

Let us find a point on y - axis which is equidistant from both the pointsA  (2, 3) and B (-4, 1).

Let this point be C (x,y).

Since the point lies on y axis the value of its coordinate is 0. We can take, x=0.

The distance between A, B and C is ,

AC =  √( 2-x)² + ( 3-y)²

     =  √( 2- 0)² + ( 3-y)²

     = √(2)² + ( 3-y)²

BC = √(-4-x)² + ( 1-y)²

     = √(-4-0)² + ( 1-y)²

     = √(-4)²+ ( 1-y)²

Equating AC = BC

√(2)² + ( 3-y)² = √(-4)²+ ( 1-y)²

(2)² + ( 3-y)² = (-4)²+ ( 1-y)²

4 + 9 + y² - 6y = 16 + 1 +  y² -2y

4y = -4

y =-1

The point on y axis which lies equidistant from the mentioned parts (2, 3) and (-4, 1) is (0,-1).