Objectives:
1. To do all kinds of
things with points in
the Cartesian plane:
distance, midpoint,
slope, equation
2. To solve an equation
for a particular
variable
Assignment:
Ignore the book
instructions. Find the
distance, midpoint,
slope and equation in
point-slope form for
these three problems:
• P. 10: 35, 38, 39
• Homework Supplement
• Read: P. 14-21; P. 30
Rectangular Coordinates
Cartesian Plane
Origin
Quadrants
Ordered Pair
Pythagorean Theorem
Midpoint
Slope
Linear Equation
How can you locate
this point
quantitatively?
Can you do it in more
than one way?
The Cartesian Coordinate
Plane is a flat place where
points hang out
• Usually called a “graph”
• Uses ordered pairs of real
numbers to locate points
• Gives a visual
representation of the
relationship between x
and y
(Also called a Rectangular Coordinate System)




1596-1650
French philosopher-etc.
Cogito Ergo Sum
A fly taught him about
the Cartesian
coordinate plane and
analytic geometry, for
which he took full credit
Find each of the following
using the two points on
the graph:
1) The distance between
the points
2) The midpoint between
the points
3) The slope of the line
between the two points
4) The equation of the line
between the points
You will be able to find the
distance between two
points
In a right triangle, the
square of the length of
the hypotenuse is equal
to the sum of the
squares of the lengths of
the legs.
c2
a2
b2
Graph 𝐴𝐵 with A(2, 1) and B(7, 8). Add
segments to your drawing to create right
triangle ABC. Now use the Pythagorean
Theorem to find AB.
If the coordinates of
points A and B are
(x1, y1) and (x2, y2),
then
AB 
x2  x1 2   y2  y1 2
To the nearest hundredth of a unit, what is the
approximate length of 𝑅𝑆, with endpoints
R(3, 1) and S(−1, −5)?
The distance between (−4, k) and (4,4) is 10
units. Find the value of k.
You will be able to find
the midpoint between
two points
If A(x1,y1) and B(x2,y2)
are points in a
coordinate plane,
then the midpoint M
of 𝐴𝐵 has coordinates
 x1  x2 y1  y2 
,


2 
 2
Find the midpoint of the segment with
3
endpoints at (−1, 5) and 2, 3 .
The midpoint C of 𝐼𝑁 has coordinates (4, −3).
Find the coordinates of point I if point N is at
(10, 2).
Slope can be used to represent an average rate
of change.
• A rate of change is how much one quantity
changes (on average) relative to another.
• For slope, we measure how y changes relative
to x.
The slope m of a
nonvertical line is the
ratio of vertical
change (the rise) to
the horizontal change
(the run).
Find the slope of the line passing through the
4
5
3
points −5, −2 and 10, −2 .
Find the value of k such that the line passing
through the points (−4, 2k) and (k, −5) has
slope −1.
You will be able to
write the linear
equation between
two points
Censored
A linear function can have many forms, pick
your favorite:
• Slope-Intercept Form: y  mx  b
• Point-Slope Form: y  y1  m  x  x1 
• Standard Form: Ax  By  C
Write the equation of the line through the
points (−2, 5) and (4, −7). Write your answer
in point-slope, slope-intercept, and standard
forms.
You will be able to solve an
equation for any variable
Page 7 of your book contains these helpful
formulas. Number them thusly:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Given any of the previous formulas, what would
it mean to solve for a particular variable?
To solve for a variable in an equation or formula
means to isolate that variable on only one side
of the equation:
variable = everything else
Solve 𝑉 = 𝜋𝑟 3 for r.
4
3
Objectives:
1. To do all kinds of
things with points in
the Cartesian plane:
distance, midpoint,
slope, equation
2. To solve an equation
for a particular
variable
Assignment:
Ignore the book
instructions. Find the
distance, midpoint,
slope and equation in
point-slope form for
these three problems:
• P. 10: 35, 38, 39
• Homework Supplement
• Read: P. 14-21; P. 30