Plot the following points:

A(0, 4) B(-3, 0) C(3, 5) D(-8, -11) E(7, -5) F(-3.5, 7.5)

Coordinate GeometryUnit Essential Question:

How can you use the coordinate plane to solve problems and demonstrate

properties?

The Coordinate Plane

Essential Question:How do you calculate distance, midpoint, and slope on a coordinate plane?

Origin x-axis y-axis Quadrants

Coordinates Positive Negative

Distance Formula

Why?

Midpoint What is the midpoint of 7 and 15?

What is the midpoint of (2, 7) and (4, 1)?

Midpoint…

Find the Midpoint:

Finding an Endpoint:

Distance? Mary walks 3 miles north and 2 miles

east. Her boyfriend John walks 2 miles south and 4 miles west. What is the straight line distance from their hearts?

Opener (Algebra Review)

Lines in the Plane

Essential Question:How do the slopes of parallel and perpendicular lines relate?

Point-Slope form (writing eqs)

Line with slope, m = -2, through (3, -5)

Slope-Intercept Form

y = mx + b

m =

b =

Example

Example:

b(egin) =

m(ove)=

Equations: m = -1/2, (-4, -1)

Point-Slope Slope Intercept

Standard Form: Ax + By = C

Example:

x-int (set y=0)

y-int (set x=0)

Transforming to Slope-Intercept

Solve for y:

b(egin) m(ove)

Example:

b(egin) =

m(ove)=

Writing Equations through 2 pts (10, 2) & (2, -2) Step 1: Find Slope

Step 2: Combine pt & slope

Equation through: (7, -4), (-5, 2) Slope:

Equation:

Horizontal & Vertical Lines

What is special?

Horizontal:

Vertical:

Horizontal & Vertical Lines

Graph the following Lines:

53 xy

23

1 xy

33 xy

Slopes of Parallel & Perpendicular Lines

Essential Question:How do the slopes of parallel and perpendicular lines relate?

Parallel Lines

Are these parallel?

Which is parallel?

Can you write the equation of a 3rd line that is parallel?

Writing equations of parallel lines

Perpendicular Lines

They are OPPOSITE RECIPROCAL slopes.b

am

a

bm

1

ba

ab

a

b

b

amm

Are they Perpendicular?

Writing Perpendicular Equations

Step 1: Perpendicular Slope:

Step 2: Combine Point & Slope:

Perpendicular Lines Write the equation of the Line through(3, 2), which is perpendicular to 3x + 2y =

-6.

Opener

Figures in the Plane

Essential Question:How can slope, distance and/or midpoint be used to establish properties of a plane figure?

Parallelograms in Quadrilaterals?

How should we draw it?› Origin & x-axis.

Labeling Vertices

Vertices of Parallelogram

Examples

Opener

Coordinate Proofs

Essential Question:How can slope, distance and/or midpoint be used to establish properties of a plane figure?

Prove the Opener? Can we PROVE that the midpoints of a

Rhombus form a Rectangle? Conveniently Plot a Rhombus, then find

its midpoints…

Coordinate Proof:

PROVE Triangle Midsegment Theorem.

Midsegment is Parallel to Base and ½ the length of the 3rd side!

Place Triangle. Find Midpoints, calculate slope and length of Midsegment.

Plan out a Proof: