Download 1-9 Coordinate Plane

Do not use a calculator to complete homework. Students who are
calculator dependent tend to make more calculating errors on tests.
After you finish an odd homework problem check the answer in
the back of the book. If the answer is incorrect, investigate why it is
wrong. When students find their errors right away it is more effective.
Don’t skip steps. Write out the support work so your eyes
can see what your brain needs to calculate. “I did it in my head”
often leads to errors.
Take notes in class, read the related lesson in the text, and
then review, review, review. It’s just not enough to sit in class for 45
minutes and then hope you have absorbed it all.
Study
tips
1-7 Logical Reasoning
1-9 Coordinate Plane
For tomorrow’s lesson you will need a colored
pencil and a ruler.
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
Logical Reasoning includes conditional statements,
deductive reasoning, and counterexamples.
A conditional statement has a hypothesis and a conclusion
and is often written in if-then form.
Deductive reasoning is a process that uses facts and
rules to reach a valid conclusion.
A counterexample is a specific example that can be
used to show that a statement is false.
Example of a conditional statement:
If the
popcorn burns, then the
heat was too high.


The part of the statement
immediately following if is
called the hypothesis.
The part of the statement
immediately following then
is called the conclusion.
Identify the hypothesis and conclusion of the statement.
If it is Friday, then the Smiths are going out to dinner.
hypothesis: it is Friday
conclusion: the Smiths are going out to dinner
Note that
“if” is not
part of the
hypotheses.
Note that
“then” is not
part of the
conclusion.
Identify the hypothesis and conclusion of each statement.
Example 1 If it is raining, then the party will be indoors.
hypothesis: it is raining
conclusion: the party will be indoors
Example 2 If 4x + 3 > 27, then x > 6.
hypothesis: 4x + 3 > 27
conclusion: x > 6
Deductive reasoning is the process of using facts, rules,
definitions, or properties to reach a valid conclusion.
You can use deductive reasoning to determine whether
a valid conclusion follows from a conditional statement.
Determine a valid conclusion that follows from the
conditional statement below. Explain your answer.
Conditional statement: If two numbers are odd, then

their
sum is even.

Given condition: The two numbers are 7 and 3.
7 and 3 are odd so the hypotheses is true.
The sum of 7 and 3 is even so the conclusion is valid.
Example 3 Determine a valid conclusion that follows
from the conditional statement below.
Conditional statement: There will be a quiz every
Wednesday.
Given condition: It is Wednesday.
Valid conclusion: _______________________
There will be a quiz.
Example 4 Determine a valid conclusion that follows
from the conditional statement below.
Conditional statement: If your test score is in the
90th percentile, then your grade is an A.
Given condition: score is 95%
Valid conclusion: ________________________
Your grade is an A.
To show that a condition is false, we can use a
counterexample. A counterexample is a specific case in
which the hypotheses is true and the conclusion is false.
Conditional statement: If a triangle has a perimeter of
3 inches, then each side measure is 1 inch.
A counterexample is a triangle with perimeter of 3 and
sides of 0.9, 0.9, and 1.2.
It takes only one counterexample to show that a
statement is false.
Example 5 Find a counterexample to show that the
conditional statement is false.
Conditional statement: If you graduate from Colina,
then you go to Westlake High.
Counterexample: _______________________
A graduate attends TOHS.
Example 6 Find a counterexample to show that the
conditional statement is false.
Conditional statement: If x + 3 > -6, then x must be
negative.
Counterexample: ___________________________
When x is 10 the statement is true
and 10 is a positive number.
Example 7 Find a counterexample to show that the
conditional statement is false.
Conditional statement: Every four-sided figure is a
rectangle.
Counterexample:
1-9 Coordinate Plane
All coordinate plane graphs must
be completed on grid paper.
A coordinate plane is formed by two real number lines that
intersect at a right angle at the origin. The horizontal axis
is the x-axis and the vertical axis is the y-axis.
y
The coordinate plane is
divided into four regions
called quadrants.
II
•
I
III IV
x
Each point in a coordinate plane corresponds to an
ordered pair of real numbers. (–2,3)
The first number
identifies the
x-coordinate and
the second
number identifies
the ycoordinate.
•
x
y
Graph the coordinate (3,4).
The first number
identifies the
x-coordinate and
the second
number identifies
the y-coordinate.
•
x
y
Example 1 Graph the coordinate (4,–2).
The first number
identifies the
x-coordinate and
the second
number identifies
the ycoordinate.
x
•
y
Example 2 Graph and label the coordinates in the same
coordinate plane:
A (3,–1), B (–4,0), C (–5,2),
D (2,–4), E (0,3), F (0,0).
C
•
E
•
B
•
•
F
•A
•D
y
x
Example 3 In which quadrant or on which axis does
each ordered pair lie?
A.
B.
C.
D.
E.
F.
G.
H.
IV
x-axis
II
IV
y-axis
origin
III
I
C
•
E
•
•
B
F
•
•
G
H
•
•A
•D
y
x
Example 4 Write the coordinates of each point.
•
D
•
G
•
B
C
•
•
F
E
•
y
•A
A. (3,–2)
B. (–4,0)
Coordinates
C. (–5,–2)
are written as
x D. (2,4)
ordered pairs.
E. (0,–3)
You must use
F. (0,0)parentheses!
G. (–4,3)
1-A12 Pages 42–44 #15–24,29–34,47–49 and
Page 57 #10–18.