Pentagon RSTUV has coordinates R(1,4),
S(5,0), T(3,4), U(1,4),
and V(3,0).
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 
as homework 
with teacher feedback 
with peer feedback 
 timed 
opportunity for revision 
with manipulatives 
with calculator 
This work sample illustrates a standardsetting
performance for the following parts of the standards:

b

Number and
Operation Concepts: Understand and use opposite, reciprocal,
raising to a power, taking a root, and taking a logarithm. 
b 
Geometry
and Measurement Concepts: Work with two dimensional figures
and their properties. 
h 
Geometry and
Measurement Concepts: Analyze figures using the concept of translation. 
k 
Geometry and
Measurement Concepts: Work with geometric measures of length. 
p 
Geometry and
Measurement Concepts: Analyze geometric figures and prove simple
things about them using deductive methods. 
b 
Problem Solving
and Mathematical Reasoning: Implementation. 
c 
Mathematical
Communication: Organize work and present mathematical procedures
and results
clearly, systematically, succinctly, and correctly. 


The basic elements of the mathematics needed
to solve this problem are:
(1) plotting given points on a coordinate
grid,
(2) finding the length of the line segment
between two points (x1,y1)
and (x2,y2)
using the distance formula based on the Pythagorean Theorem:
distance =
(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 xcoordinate
in the original set is 3, and the most negative ycoordinate 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.)
