Locus of Equidistant Points

Author:
Zainab Nandawula

1) What is the locus equidistant from a fixed point?

  1. To determine the locus equidistant from a fixed point, we need to draw a set of points that are always the same distance away from a fixed point:
Imagine 10 Eskimos in an igloo with a fireplace at the center. How can they arrange their seats so that they all receive the same amount of warmth? Use the "point" tool to draw the seats and the "cm" tool to measure distance.

What is the locus equidistant from a fixed point?

Describe the figure formed (or the path that is traced) by the set of points that are always equidistant from a fixed point?

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3) What is the locus equidistant from a fixed line?

  1. To determine the locus equidistant from a fixed line, we need to draw a set of points that are always the same distance away from a fixed line:
Imagine you're a housing developer tasked with building 10 apartments around a city's sole subway line. Design/ draw an arrangement of the apartments so that that they are all the same distance from the subway line?

What is the locus Equidistant from a Fixed Line?

Describe the figure formed (or the path that is traced) by the set of points that are always equidistant from a fixed line?

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5) What is the locus equidistant from two points?

  1. To determine the locus equidistant from two points, we need to draw a set of points that are always the same distance away from two points:
Imagine that BPS wants to build a library that it is exactly the same distance from both BLA and BLS. Draw at least 6 potential locations for this library.

What is the locus Equidistant from Two Points

Describe the figure formed (or the path that is traced) by the set of points that are always equidistant from two points?

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7) What is the locus equidistant from two parallel lines?

  1. To determine the locus equidistant from two parallel lines, we need to draw a set of points that are always the same distance away from two parallel lines:
Imagine driving along a very narrow but straight road. How can you drive in such a way that you are not too close to the curb on either side? (always the same distance away from either curb)? Draw the path you should take.

Equidistant from two parallel lines

What kind of path is traced by the points you drew? In other words, what is the locus of points that are equidistant from two parallel lines?

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9) What is the locus equidistant from the sides of an angle?

  1. To determine the locus equidistant from the sides of an angle, we need to draw a set of points that are always the same distance away from the sides of an angle:
Consider the sides of the letter, L which form a right angle as shown below. Draw the set of points that are always the same distance from the sides KL and LM.

What is the locus equidistant from the sides of an angle?

Describe the figure formed (or the path that is traced) by the set of points that are always equidistant from the sides of an angle.

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SUMMARY

Write two sentences about what you have learned today. Address the following topics:

  1. What is meant by "locus"?
  2. How do we use locus in geometry?
  3. What is the locus equidistant from a :
  • a fixed line
  • a fixed point
  • two parallel lines
  • two points

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