Pentagon RSTUV has coordinates R(1,4),
S(5,0), T(3,-4), U(-1,-4),
a) On graph paper, plot Pentagon RSTUV.
b) Determine if Pentagon RSTUV is a regular
pentagon. Show all your work and explain your answer in sentence form.
c) Describe a translation that would place
Pentagon RSTUV completely in the first quadrant of the graph.
|This sample of student work was produced
under the following conditions:
| - alone
||in a group
| - in class
|with teacher feedback
||with peer feedback
||opportunity for revision
This work sample illustrates a standard-setting
performance for the following parts of the standards:
Operation Concepts: Understand and use opposite, reciprocal,
raising to a power, taking a root, and taking a logarithm.
and Measurement Concepts: Work with two dimensional figures
and their properties.
Measurement Concepts: Analyze figures using the concept of translation.
Measurement Concepts: Work with geometric measures of length.
Measurement Concepts: Analyze geometric figures and prove simple
things about them using deductive methods.
and Mathematical Reasoning: Implementation.
Communication: Organize work and present mathematical procedures
clearly, systematically, succinctly, and correctly.
The basic elements of the mathematics needed
to solve this problem are:
(1) plotting given points on a coordinate
(2) finding the length of the line segment
between two points (x1,y1)
using the distance formula based on the Pythagorean Theorem:
(3) using the fact, from the definition of
a regular polygon, that all side lengths of a regular pentagon must
be equal, and
(4) specifying a translation T(4,5)
in the plane as an operation that shifts every point in the plane +4
units in the x direction and +5 units in the y direction.
(Notice that the most negative x-coordinate
in the original set is -3, and the most negative y-coordinate is -4. Hence
T(4,5) is the shortest translation that maintains
integer coordinates and that sends the figure to a position entirely within
the first quadrant.)