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In the diagram at right, the point is the same distance from as it is from . There are many possibilities for . Algebraically, what do they have in common?

  1. What is the distance from to ?

    Do you remember the equation to determine the distance between two points?

  2. What is the distance from to ?

    Use the same equation as in part (a).

  3. Write the equation that states that the two expressions in (a) and (b) are equal and simplify.

    Set your two distance equations from parts (a) and (b) equal to each other.
    Then simplify this larger equation until it is in form.

  4. What is the specific name of the geometric object represented by your equation from part (c)?

    Try graphing your answer from part (c).
    How does this new graph relate to the original line?

A closed line segment between the points, (negative 3, comma, 4) and (2, comma negative 1). There is another point on the graph located about (2, comma 4) labeled, (x, comma y).