Transcript Planning Parks Problem 1.3 - Westville School District

The Euclid city council is planning to develop parks with
geometric shapes. For some of the parks, the city council has
given constraints to the parks designers. For example, one of the
parks must have a border that includes the vertices (1, 1) & (4, 2).
10
8
6
4
Gas Station
Stadium
2
(4, 2)
(1, 1)
Greenhouse
-10
City Hall
-5
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Planning Parks
Problem 1.3
Police Station
-6
-8
Cemetery
10
If the park with the given vertices is to be a square,
what could the coordinates of the other two
vertices be? Give two answers.
8
6
4
Gas Station
Stadium
2
(4, 2)
(1, 1)
Greenhouse
-10
City Hall
-5
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery
10
If the park with the given vertices is to be a square,
what could the coordinates of the other two
vertices be? Give two answers.
8
6
There are only 3
possible squares.
4
Gas Station
Stadium
2
(4, 2)
(1, 1)
Greenhouse
-10
City Hall
-5
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery
10
If the park with the given vertices is to be a
nonsquare rectangle, what could the coordinates of
the other two vertices be? Give two answers.
8
6
4
Gas Station
Stadium
2
(4, 2)
(1, 1)
Greenhouse
-10
City Hall
-5
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery
10
If the park with the given vertices is to be a nonsquare rectangle, what could the coordinates of the
other two vertices be? Give two answers.
8
6
-10
There are only
many possible nonsquares. You can
Stadium
just keep stretching
the green one
forever
to make a
Greenhouse
new one.
-5
4
Gas Station
2
(4, 2)
(1, 1)
City Hall
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery
If the park with the given vertices is to be a right
triangle, what could the coordinates of the other
two vertices be? Give two answers.
10
8
6
4
Gas Station
Stadium
2
(4, 2)
(1, 1)
Greenhouse
-10
City Hall
-5
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery
10
If the park with the given vertices is to be a right
triangle, what could the coordinates of the other
two vertices be? Give two answers.
8
6
-10
There are only
many possible right
triangles. You can
Stadium
just keep stretching
the green one
forever
to make a
Greenhouse
new one.
-5
4
Gas Station
2
(4, 2)
(1, 1)
City Hall
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery
10
If this park is to be a parallelogram that is not a rectangle,
what could the coordinates of the other two vertices be? Give
two answers.
8
6
4
Gas Station
Stadium
2
(4, 2)
(1, 1)
Greenhouse
-10
City Hall
-5
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery
10
If this park is to be a parallelogram that is not a rectangle,
what could the coordinates of the other two vertices be? Give
two answers.
8
6
-10
There are only
many possible
parallelograms. You
can just keep
stretching the green
one foreverGreenhouse
to make
a new one. -5
4
Gas Station
Stadium
2
(4, 2)
(1, 1)
City Hall
Art Museum
5
10
-2
Animal shelter
-4
Hospital
Police Station
Cemetery