Warm Up
1. Anna started with 270 in her bank account. If she
deposits $40 each week after getting paid, after
how many weeks will it take for her to have at least
$500? Write your answer in a complete sentence.
2. Solve
3. Solve and GRAPH
HW Check 1. 11
FORMULAS!!!
Pythagorean Theorem & Distance
The Pythagorean
Theorem
Remember right triangles?
Special Names for Right Triangles
Hypotenuse!
Legs!
The Pythagorean Theorem
In any right triangle, the sum of the squares of
the legs is equal to the square of the
hypotenuse.
c
a
b
1) Find the length of the unknown side
of the triangle:
15 m
8m
2) Find the length of the unknown side
of the triangle:
5 yd
12 yd
Pythagorean Triples
Three side lengths that would form a right
triangle.
The two smaller numbers are always “a” and “b”
Ex) 3) Are the following side lengths
Pythagorean triples?
a) 8, 10, 4
b) 5, 3, 4
4) How far does the catcher have to
throw to reach second base?
5) Which 3 of the following side
lengths could be used to create a right
triangle?
11, 5, 12, 9, 13
Literal Equations
A literal equation is an equation with more
than one variable. Formulas are literal
equations.
Sometimes we need to solve a formula for a
specific variable
Ex 6) Solve
for b.
Word Problems
7) John leaves school to go home. He walks 6
blocks North and then 8 blocks west. How far
is John from the school?
8) A suitcase measures 24 inches long and 18
inches high. What is the diagonal length of
the suitcase to the nearest tenth of a foot?
Remember plotting coordinates?
The Coordinate Plane
An Ordered Pair
identifies the
location of a point.
Practice
Plot the following coordinates:
1. (-2, 3)
2. (4, -1)
3. (1, 1)
4. (-3, -4)
5. (0, 0)
9) How can we find the distance
between the two points?
.
(-3, -2)
.
How long is this leg?
(4, 6)
We can use the
Pythagorean Theorem!
What about this leg?
The Distance Formula
.
(-3, -2)
.
(4, 6)
The distance formula uses
the Pythagorean Theorem to
find the distance between
two points.
It has the coordinates for
each point built in, so it finds
the length of each “leg” for
you!
The Distance Formula
.
(-3, -2)
.
(4, 6)
Use the distance formula
to find the distance
between the two points.
10)
(-5, 5)
Use the distance formula
to find the distance
between the two points.
.
.
(3, -4)
Word Problem
11) On a map’s coordinate grid, Walt
City is located at (-1, -3) and Smithville
is located at (4, 9). How long is a
train’s route as the train travels along
a straight line from Walt City to
Smithville? (One map unit equals one
mile.)
Coming up….
HW tonight – 1.12
Quiz 1.3 Friday!