Transcript Section 6.7

CP Geometry
Mr. Gallo
Classifying Polygons in the Coordinate
 Use three formulas:
Formula
When to Use it
Distance Formula
d
 x2  x1    y2  y1 
2
2
Midpoint Formula
  x1  x2   y1  y2  
M 
,

2
2


Slope Formula
y y
m 2 1
x2  x1
To determine whether:
• Sides are congruent
• Diagonals are congruent
To determine:
• Coordinates of midpoint of side
• Whether diagonals bisect each other
To determine whether:
• Opposite sides are parallel
• Diagonals are perpendicular
• Sides are perpendicular
Is ∆𝑅𝑆𝑇 scalene, isosceles or equilateral?
Use the distance formula
to find the side lengths:
RS 
 3  4    3  1
2
6
2
4
S
RS  7 2  22  53  7.28
2
ST 
 3  1   3  3
2
R
2
ST  22  62  40  6.32
-5
5
-2
RT 
1  4    3  1
2
2
RT  52   4   41  6.4
T
-4
2
-6
∆𝑅𝑆𝑇 is a scalene triangle
Is parallelogram ACBD a rhombus? Explain.
Use the slope formula to find
the slopes of the diagonals:
6
4
C
B
2
-5
5
35
8
4
m of CD 


2  4 6
3
24 6 3
m of AB 
 
53 8 4
-2
A
Product of
slopes:
-4
3 4
    1
4 3
D
-6
It is a rhombus
What is the most precise classification of the
quadrilateral formed by connecting the midpoints of
the sides of the isosceles trapezoid?
Use the midpoint formula to
find the midpoints of the sides:
6
  3  4   3  2  
M of OL  
,

2
2 

M of OL   3.5, 0.5 
 3  4 3  2 
M of NM  
,

2
2


M of NM   3.5, 0.5 
M of LM   0, 2 
M of NM   0,3
4
(0,3)
O
N
P
2
Q (3.5,0.5)
(-3.5,0.5) S
-5
5
R
L
-2
(0,-2)
-4
-6
M
Use the distance formula to find the side lengths:
RS 
2
2
0

3.5


2

0.5

 
  4.3 RQ 
SP 
2
2
0

3.5

3

0.5

 
  4.3
2
2
3.5

0

0.5

2

 
  4.3
6
PQ 
 0  3.5   3  0.5
2
2
 4.3
4
Find the slopes of the sides:
0.5  2
m of RS 
 .714
3.5  0
0.5  2
m of RQ 
 .714
3.5  0
Product of slopes:
.714 .714   .51
It is a rhombus
(0,3)
O
N
P
2
Q (3.5,0.5)
(-3.5,0.5) S
-5
5
R
L
-2
(0,-2)
-4
-6
M
Complete Got It? #1, 2 & 3 p.401-402
Scalene
2. Yes, 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑀𝑁 = 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑃𝑄 = −3 and
1
𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑁𝑃 = 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑀𝑄 =
1.
3
b.
c.
Yes; 𝑀𝑁 = 𝑃𝑄 = 𝑁𝑃 = 𝑀𝑄 = 10
3
4
Yes; 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝐴𝐵 = and 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝐵𝐶 =
Therefore, ∠𝐵 is a right angle and ∆𝐴𝐵𝐶 is a right
triangle.
3. Rhombus
a.
4
− .
3
Side length is 13
Homework: p.403 #22-30 even, 45-48