Question

Find the point (0,b) on the y-axis that is equidistant from the points (4,4) and (3,−2).

Answer 1

Okay so our equation is basically: |(0,b)(4,4)| = |(0,b)(3,-2)| right? Do you know the formula for finding the distance between points?

Answer 2

Yes, I know the distance formula

Answer 3

So whats the distance between (0,b) and (4,4)?

Answer 4

You can get it in terms of b.

Answer 5

sqrt(16+(4-b)^2)

Answer 6

Now what's the distance between (0,b) and (3,-2)? Again in terms of b

Answer 7

@lhunter /Have you got the solution?

Answer 8

The length of a line segment with endpoints A(a, b) and B(c, d) is given by

L = √[(c − a)² + (d − b)²]

Point M(0, b) is equidistant from A(4, 4) and B(3, -2).

|AM| = |BM|

√[(4 − 0)² + (4 − b)²] = √[(3 − 0)² + (-2 − b)²]

squaring both sides, we obtain

16 + (4 − b)² = 9 + (-2 − b)²

16 + 16 − 8b + b² = 9 + 4 + 4b + b²

19 = 12b

b = 19/12

∴ the point (0, 19/12) is equidistant from (4, 4) and (3, -2).