What is a locus? A locus is usually found a series of point that form a curve or a surface that meet a set of criteria or a circumstance. In most cases the point will meet up in such a fashion that they form a design where they are an equidistance from another geometric figure. They align their behavior in such a way that they form set geometric structures. You will often find them used to form circles, parallel lines, perpendicular bisectors, and they are used to manipulate measures on intersecting lines.
You will be given a scenario where two parallel lines are a fixed distance between a third value. Your goal is to find the position of that value. This is actually the math concept that the game Battleship is entirely built on. Instead of firing blank missiles in to the water here, we use our understanding of angle bisectors to find that third value.

These worksheets explain how to find the locus of points equidistant from points and parallel lines. Your students will use these worksheets to practice calculating the locus of points equidistant from other points, parallel lines, and intersecting lines.

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This worksheet explains how to describe the locus of a third pin so that it is always the same distance from each intersecting pin given the value of the angle. A sample problem is solved, and two practice problems are provided.

Students will practice this skill by working on problems such as: Describe the locus of a third row of stones so that it is always the same
distance from each intersecting rows of stones making an angle of 52° . Ten problems are provided.

Example problem: Harry rides so that he is always the same distance from each intersecting field
forming an angle of 36°. Harry’s path is at 18° from each intersecting field. Ten problems are provided.

A good way to see if students have mastered this skill. Three problems are provided, and space is included for students to copy the correct answer when given.

This worksheet explains how to find the locus of points equidistant from two parallel lines. A sample problem is solved, and two practice problems are provided.

We get a bit more abstract with the problems on this review sheet. Example: Describe the locus of the center of the wheel of a truck that is moving along a
straight, level track. Six practice problems are provided.

We begin with simple problems and advance to more advanced problems. Example: Describe the locus of a board that has to be kept equidistant from 2 parallel
boards. Ten problems are provided.

Students will find the locus of points equidistant from two parallel lines. Three problems are provided, and space is included for students to copy the correct answer when given.

This worksheet explains how to find the locus of points equidistant from two points. A sample problem is solved, and two practice problems are provided.

These problems focus more on application. Example: Two poles are 8 meters apart. A wire is to be tied such that the distance from
any point on the wire to each pole is always the same distance. Describe
where the wire should be tied. Ten problems are provided.

This is where the architect in you shines. Example exercise: Two pillars are 30 m apart. A net is to be placed such that the distance from any
point on the net to each pillar is always the same distance. Describe where the
net should be placed. Ten problems are provided.

We work off of given points to match a condition. The locus of points equidistant from the points (13,-5) and (13, 7) is a line whose
equation is y = 1. Example: Six practice problems are provided.

Students will find the locus of points equidistant from two points. Three problems are provided, and space is included for students to copy the correct answer when given.

Why are parallel lines equidistant?

First of all, before explaining this, we should first review what is meant by equidistant and parallel lines. Equidistant means that a similar distance, it's derived from its prefix "equi," meaning equal and suffix "distant" which implies distance. Parallel lines are equidistant always from each other because every point on any line is still equally distant from the facts on the other parallel line. While on the other hand, when two lines have the same slope, they are called similar to each other, and they also have different y-intercept.
How? You would ask, well, it is essential to keep in mind that when people are talking about "distance" in the geometry of Euclidean, they are always referring to the very shortest distance. The shortest distance among a point and line is the distance of the perpendicular line from the other end to the bar. If the length of the two points is not equidistant, then it cannot be considered as a parallel line, sometimes the difference I so less that they might look like they are similar lines, but they are actually not and can meet at some point after covering some distance.