Math 130

2.1 – Rectangular Coordinates and Graphs

Rectangular coordinate system (also called Cartesian coordinate system):

The Distance Formula

Suppose you’re looking for the distance from point at ( ) to point at ( ).

Can use Pythagorean Theorem to get the distance formula:

( ) √( ) ( )

Ex 1.

Find the distance between ( ) and ( ).

The Midpoint Formula

Midpoint formula: (

)

Ex 2.

Find the midpoint of the segment with endpoints ( ) and ( ).

Ex 3.

Find the endpoint of a segment with one endpoint ( ) and midpoint ( ).

Graphing Equations

The graph of an equation is the set of all ordered pairs that solve the equation.

Ex 4.

Show that the ordered pair ( ) solves the equation .

Ex 5.

Find at least two ordered pairs that are solutions to .

Ex 6.

Find at least two ordered pairs that are solutions to √ .

-intercept – the -coordinate of a point where graph intersects -axis

-intercept – the -coordinate of a point where graph intersects -axis

What do all points on the -axis have in common?

What do all points on the -axis have in common?

So, to find the -intercept, set and solve for .

And to find the -intercept, set and solve for .

Ex 7.

Find the intercepts of .

Ex 8.

Find the intercepts of √ .

How to graph equation by plotting points

1. Find intercepts.

2. Find additional ordered pairs as needed.

3. Plot ordered pairs.

4. Connect points with smooth line or curve.

Ex 9.

Graph .

Ex 10.

Graph √ .

Q: What can you catch but not throw?