May 10, 2013 and May 18 - May 28, 2015
Treasure Hunt Experience Closure Reflection
What did we discover in looking for treasure?
In each treasure hunt experience we were given a set of conditions to help us find where
our treasure could be. We found a collection of locations which satisfied the conditions
and these points would form circles, lines or other curves such as a parabola, ellipse and
hyperbola. What we discovered is called a locus of points.
A locus of points is a collection of points, all of which satisfy some specific condition.
Big Idea: Loci ( plural of locus is pronounced “low sigh”) is essentially the study of
curves.
Our locus was a collection of locations where our treasure could be.
1. The Circle
The treasure is 100 feet from a tree in a field. Where can the treasure be?
The locus of points that are a set distance from a given point A is a circle.
2. Two Parallel Lines
The treasure is buried 100 feet from a straight fence in a field
The locus of points that are a set distance from a given line A is two parallel lines,
one on each side of the given line.
3. Two Concentric Circles
The treasure is buried 100 feet from a circular fence in a field.
The locus of points that are a set distance from a given circle is two circles, one
on each side of the given circle.
4. A Perpendicular Bisector
The treasure is buried so that it is equally distant from 2 trees in a field.
The locus of points equidistant from two points is the perpendicular bisector of
the line segment that joins the two given points.
5. Two Angle Bisectors
The treasure is buried equally distant from two straight fences which intersect
each other at a random angle in the field.
The locus of points equidistant from two intersecting lines is the two angle
bisectors of the given lines.
6. The Parabola
The treasure is buried an equal distance from a tree and a straight fence and the
tree is not on the straight fence. We need to survey the field for this one!
The locus of points equidistant from a point and a straight line is a parabola.
7. The Ellipse
The treasure is buried equally distant from a tree planted inside a circular fence
and the circular fence. We need to survey the field with 1 cm. concentric circles
inside the circular fence and 1 cm. concentric circles around the tree to help us
find this one!
The locus of points equidistant from a given circle and a point inside the circle is
an ellipse.
8. The Hyperbola
The treasure is buried equally distant from two trees which are planted equally
distant from a circular fence in the middle of a field, and equally distant from the
fence.
The locus of points equidistant from a circle and two points equidistant from the
circle is a hyperbola.