1Lattice Point PolygonsProblem
Robert J. Reed, Brown Middle School, Newton, MA
1. Plot the points A (1, 2), B (4, 6), C (8, 3), and D (5,1)
O
on the grid shown here, and connect them to create
quadri-lateral ABCD.
2. What kind of quadrilateral is ABCD? Prove your claim.(That
is, show that ABCD is what you say it is.)
The coordinates of the vertices of ABCD were all integers,
andall of those integers were dierent .
3. Using the same rulesonly integer coordinates and, for Your
work will be judged on thequantity, quality, appearance,
andcomplexity of your polygons, andon how clearly you show how
youknow what each polygon really is.
any one polygons vertices, no integer repeatedtry tomake other
polygons, like a right trapezoid, isosceles trape-zoid, scalene
triangle, kite, and so on.
Problems with a Point: March 16, 2001 c EDC 2000
Lattice Point Polygons: Solutions 1
Solutions
1.
O
A
B
C
D
2. Quadrilateral ABCD is a square. All four sides are diag-onals
of 3 4 rectangles, so they are all 5 units long. Byrotating the 3 4
rectangles and noticing the eect on thediagonals, or by comparing
the slopes (4
3and 3
4) of the
sides of ABCD, we see that the sides are perpendicular.
3. This is part of one students solution. One of the gurescan
not be allowed, because it violates the rules.
A
K
E
D
F
B
C
G
J
IH
L
20
10
13
5
( 9, 8)
( 8, 3)
( 12, 6)
5 13
5
( 5, 5)
(14,3)
(11,7)
(11, 6)
(7, 2)
(5, 4)
(1, 11)
2
2
4
2
(9, 8)
Problems with a Point: March 16, 2001 c EDC 2000
