Key
Section 7.9
Classifying Quadrilaterals Using Coordinates
THE SLOPE FORMULA:
THE DISTANCE FORMULA:
y 2 − y1
x 2 − x1
m=
d = ( x2 − x1 ) 2 + ( y2 − y1 ) 2
Graph each of the following coordinates. Then determine what shape the quadrilateral is
using the slope and distance formulas.
1.
R(-1, 3) O(2, 7) N(5, 3) Y(2, -1)
a.
How can we use the slope formula to
determine if a quadrilateral is a
parallelogram?
sides have the
0
A•N
•
•
;
c.
RV
b.
Use the slope formula to verify that the
quadrilateral is a parallelogram.
mrate
months
Mm=¥
Mart
Parallelogram
because
have the
slopes
ifthedigondsare
Congruent
so
they
are
sides
parallel
.Ifno+¥→No+a
.
.
diagonals
not
are
congruent
.
How can we use the distance formula to determine if a quadrilateral is a rhombus?
Determine
if all 4
side
congruent
are
.
.
Using the distances, determine if this parallelogram is a rhombus. Explain why or why not.
don=F35taE5
don
(
5-232+(3-7)
-
Yes ,aH4 sides
g.
opposite
rectangle
dox=r#te=8
Notarectangkbecawethe
f.
same
45
-
Using the distances, determine if this parallelogram is a rectangle. Explain why or why not.
drn.it#ptc33p=G
e.
slope
same
If we know that a quadrilateral is a parallelogram, how can we determine if a quadrilateral is
a rectangle using the distance formula?
If~=→ Rectangle
Determine
d.
show opposite
-2=5
are
dNY=
2-55+4-39=5
-
FEED
drive
congruent
(
.
Is this parallelogram a square? Explain why or why not.
No
,
itisnotarectangkanda
rhombus
.
--
5
.
2.
J(-6, -2) O(-3, 4) S(5, 0) E(2, -6)
a.
How can we use the distance formula to
determine if a quadrilateral is a
parallelogram?
Show that both pairs of opposite
side
~]
O
/
J
dos
da
of
=FsEPtco.4I= 8.9
ftp.go#s.9
6.7
Thatch
=
'
.
=
Parallelogram
because
have the
lengths
opposite
are
same
congruent
so
(
perpendicular
have
=
Mos
65=2
=
St
=
=
45=+2
-
Yes slopes
opposite
of
,
MJE
2
=
-
connecting
perpendicular
angles
corner
making ante
sides
45=-15
are
right angles
.
How can we use the slope formula to determine if a quadrilateral is a rhombus?
Show that
the
diagonals
reciprocal slopes )
(
perpendicular
are
have
opposite
Using the slopes, determine if this parallelogram is a rhombus. Explain why or why not.
II
mo*
,
=¥=
No the slopes
are
,
not
are
g.
sides
Using the slopes, determine if this parallelogram is a rectangle. Explain why or why not.
MSE
f.
6.7
they are
If we know that a quadrilateral is a parallelogram, how can we determine if a quadrilateral is
a rectangle using the slope formula?
Msa
e.
=
drs=cTHtC6oY=
E
Show that connecting side
reciprocal slopes )
d.
.
Use the distance formula to verify that the
quadrilateral is a parallelogram.
•
•
c.
b.
congruent
are
-2
mss
not opposite
perpendicular
=
SIT
reciprocals
.
Is this parallelogram a square? Explain why or why not.
No
,
it
is
not
a
rectangle and
a
rhombus
.
=
so
if
the diagonals
.
3.
M(5, -2) A(-1, -4) T(-3, 2) H(3, 4)
a.
:
mm
:¥¥
:I¥¥nF
¥I
:
both pairs of opposite
are parallel
•m
•
b.
Use the slope formula to verify that the
quadrilateral is a parallelogram.
.
Using the distances, determine if this parallelogram is a rectangle. Explain why or why not.
m=tF5Pta2
dHa=
(
-8.9
aD2tC4-f4D2=8Q
#
3-
Yes because the
c.
sides
diagonals
to
congruent
are
each other
Using the slopes, determine if this parallelogram is a rhombus. Explain why or why not.
Mtm=Ijt¥=¥=
-
the
Yes the slopes of
are
opposite reciprocals
+2
,
diagonals
3-
th
ofeachottermeaningthatttey
MHa=4±D=§=2
d.
are
perpendicular
to each other
Is this parallelogram a square? Explain why or why not.
.
Yes because
itisbotha
rhombus and
a
rectangle
.
.
IT’S A TRAP!!!
4.
T(-3, -4) R(-2, 1) A(2, 4) P(5, 2)
a.
Use the slope formula to verify that the
quadrilateral is NOT a parallelogram.
:¥¥
II.
T•
in
Both pairs of opposite
it
not parallel so
are
be
b.
parallelogram
a
side
on
has
lines
.
one
pair
of parallel
Is the quadrilateral that you graphed an isosceles trapezoid? Explain why or why not.
dRT=T2t3D2CEP
dap
No
.
T
5-25+(2-4)
=
The
not
non
2
parallel
.
congruent
.
't
Explain why the shape is trapezoid.
It
c.
in
:I¥
.
5
=
I
.
=3 6
.
sides
of
the
trapezoid
are