Using Slopes and Distances to Prove Relationships
a) Rectangle ABCD
A (-2,4)
B (-2,1)
C (4,1)
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A
D ( ____ , ____ )
C
B
b) Parallelogram ABCD
A (0,0)
B (4,1)
C (6,3)
C
D ( ____ , ____ )
B
A
c) Rectangle ABCD
A (2,-1)
B (6,1)
C (5,3)
D ( ____ , ____ )
d) Isosceles ABC
Vertex B
A (1,0)
B (4,4)
C (1, ____ )
Using Slopes and Distances to Prove Relationships
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Prove or disprove that quadrilateral ABCD is a rectangle where A(2,-5), B(8,-3), C(7,0), and D(1,-2) are its
vertices.
Determine the most specific name for quadrilateral ABCD with vertices at
A(-3,0), B(1,2), C(0,4), and D(-4,2).
Using Slopes and Distances to Prove Relationships
HOMEWORK
1. Determine the missing vertex or coordinates of the shape.
a) Square ABCD
b) Rectangle ABCD c) Isosceles ABC
A (0,0)
A (3,-1)
Vertex A
B (4,0)
B (3,-7)
A (8,-2)
C (4,4)
C (-1,-7)
B (6,5)
D ( ____ , ____ )
D ( ____ , ____ )
C ( ____ , 5)
2. Determine the missing vertex or coordinates of the shape.
a) Rhombus ABCD
b) Parallelogram
c) A 5,12,13 Right
ABCD
ABC
A (-7,9)
A (-2,-2)
A (-3,3)
B (-9,5)
B (0,-3)
B (9,3)
C (-7,1)
C (5,-2)
C ( 9, ____ )
or
D ( ____ , ____ )
D ( ____ , ____ )
C ( 9, ____ )
3. Determine the missing vertex or coordinates of the shape.
a) Square ABCD
b) Parallelogram ABCD
A (0,0)
A (0,0)
B (5,0)
B (2,5)
C (5,5)
C (7,6)
D ( ____ , ____ )
D ( ____ , ____ )
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Using Slopes and Distances to Prove Relationships
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4. Determine the required information.
Determine the slope of
AB and then find the
coordinates of two
points that would form
B
a  line to AB through B.
slope AB = ______
C ( _____ , _____ )
A
or
C ( _____ , _____ )
5. Jeff is instructed to find vertex D of parallelogram ABCD, where A(0,0), B (6,0), C (4,7). Jeff says “I would
find vertex D using slope.” Explain how slope would be used to find vertex D.
6. Determine the value for g such that AB is perpendicular to CD . A (-4,-2) B (2,1) C (-3,2) D (2,g)
7. Determine the most specific name for quadrilateral ABCD with vertices,
A(2,-1), B (8,1), C (7,4) and D (1,2).
8. Determine the most specific name for the quadrilateral ABCD with vertices,
A (0,0), B (3,4), C (0,8) and D (-3,4).
Using Slopes and Distances to Prove Relationships
9. Jeff is asked to find the final vertex C so that an isosceles is
formed when A is the vertex, A (-2,2) B(2,-6). Jeff comes up
with C (-6,-6).
a) Is Jeff correct? Prove it.
b) Is that the only point that would have created an isosceles
triangle? Explain.
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