plot the following points:
DESCRIPTION
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 Geometry. Unit Essential Question: How can you use the coordinate plane to solve problems and demonstrate properties?. The Coordinate Plane. Essential Question: - PowerPoint PPT PresentationTRANSCRIPT
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Plot the following points:
A(0, 4) B(-3, 0) C(3, 5) D(-8, -11) E(7, -5) F(-3.5, 7.5)
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Coordinate GeometryUnit Essential Question:
How can you use the coordinate plane to solve problems and demonstrate
properties?
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The Coordinate Plane
Essential Question:How do you calculate distance, midpoint, and slope on a coordinate plane?
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Origin x-axis y-axis Quadrants
Coordinates Positive Negative
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Distance Formula
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Why?
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Midpoint What is the midpoint of 7 and 15?
What is the midpoint of (2, 7) and (4, 1)?
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Midpoint…
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Find the Midpoint:
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Finding an Endpoint:
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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?
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Opener (Algebra Review)
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Lines in the Plane
Essential Question:How do the slopes of parallel and perpendicular lines relate?
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Point-Slope form (writing eqs)
Line with slope, m = -2, through (3, -5)
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Slope-Intercept Form
y = mx + b
m =
b =
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Example
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Example:
b(egin) =
m(ove)=
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Equations: m = -1/2, (-4, -1)
Point-Slope Slope Intercept
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Standard Form: Ax + By = C
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Example:
x-int (set y=0)
y-int (set x=0)
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Transforming to Slope-Intercept
Solve for y:
b(egin) m(ove)
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Example:
b(egin) =
m(ove)=
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Writing Equations through 2 pts (10, 2) & (2, -2) Step 1: Find Slope
Step 2: Combine pt & slope
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Equation through: (7, -4), (-5, 2) Slope:
Equation:
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Horizontal & Vertical Lines
What is special?
Horizontal:
Vertical:
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Horizontal & Vertical Lines
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Graph the following Lines:
53 xy
23
1 xy
33 xy
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Slopes of Parallel & Perpendicular Lines
Essential Question:How do the slopes of parallel and perpendicular lines relate?
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Parallel Lines
Are these parallel?
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Which is parallel?
Can you write the equation of a 3rd line that is parallel?
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Writing equations of parallel lines
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Perpendicular Lines
They are OPPOSITE RECIPROCAL slopes.b
am
a
bm
1
ba
ab
a
b
b
amm
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Are they Perpendicular?
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Writing Perpendicular Equations
Step 1: Perpendicular Slope:
Step 2: Combine Point & Slope:
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Perpendicular Lines Write the equation of the Line through(3, 2), which is perpendicular to 3x + 2y =
-6.
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Opener
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Figures in the Plane
Essential Question:How can slope, distance and/or midpoint be used to establish properties of a plane figure?
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Parallelograms in Quadrilaterals?
How should we draw it?› Origin & x-axis.
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Labeling Vertices
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Vertices of Parallelogram
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Examples
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Opener
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Coordinate Proofs
Essential Question:How can slope, distance and/or midpoint be used to establish properties of a plane figure?
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Prove the Opener? Can we PROVE that the midpoints of a
Rhombus form a Rectangle? Conveniently Plot a Rhombus, then find
its midpoints…
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Coordinate Proof:
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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.
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Plan out a Proof: