8.5 Coordinate Geometry
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8.5 Coordinate Geometry
description
8.5 Coordinate Geometry. 3 2. slope of EF =. 3 5. slope of GH =. 3 5. slope of PQ =. –2 3. 2 3. slope of CD = or –. 3 –3. slope of QR = or –1. Example 1: Finding Perpendicular and Parallel Lines. Which lines are parallel? Which lines are perpendicular?. - PowerPoint PPT Presentation
Transcript of 8.5 Coordinate Geometry
8.5
Coordinate Geometry
Slopes of Parallel and Perpendicular Lines
• Any two nonvertical lines with equal slopes are parallel. Any two vertical lines are parallel.
• Any two nonvertical lines whose slope have a product of –1 are perpendicular. Vertical and horizontal lines are perpendicular.
Example 1: Finding Perpendicular and Parallel Lines
Which lines are parallel? Which lines are perpendicular?
slope of EF = 32
slope of GH = 35
slope of PQ = 35
slope of QR = or –1 3 –3
2 3
slope of CD = or – –2 3
Step 1 Find the slope of each line.
Example 1 Continued
The slopes are equal. =35
35
The slopes have a product
of –1: • – = –132
2 3
GH || PQ
EF CD
Which lines are parallel? Which lines are perpendicular?Step 2 Compare the slopes.
Check It Out! Example 2
A
C
B
D
F
E
K
JH
G
Which lines are parallel? Which lines are perpendicular?
slope of AB = or –6 4
–3 2
slope of CD = –2 3
slope of EF = or –4 6
–2 3
slope of GH = 23
slope of JK = or 1 3 3
Step 1 Find the slope of each line.
CD || EF
GH AB
A
C
B
D
F
E
K
JH
G
Check It Out! Example 2 Continued
Which lines are parallel? Which lines are perpendicular?
The slopes are equal. =–2 3
–2 3
The slopes have a product
of –1: • – = –123
3 2
Step 2 Compare the slopes.
A polygon is a closed plane figure formed by three or more line segments called sides. Each side meets exactly two other sides, one on each end, in a common endpoint. Quadrilaterals are polygons with four sides and four angles. Quadrilaterals with certain properties are given additional names.
Example 3: Using Coordinates to Classify Quadrilaterals
Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral.
A(3, –2), B(2, –1), C(4, 3), D(5, 2)
parallelogram
CD || BA and BC || AD
R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2)
parallelogram, rectangle, rhombus, square
Check It Out! Example 4
Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral.
TU || SR and ST || RU
TURU, RURS, RSST and STTU
2 pairs of parallel sides, 4 right angles.
Rectangle JKLM with J(– 1, 2), K(4, 2), and L(4, –1)
Step 2 Complete the figure to find the missing vertex.
Check It Out! Example 5
Find the coordinates of the missing vertex.
J
L
K
M
Step 1 Graph and connect the given points.
The coordinates of M are (–1, –1).
