Download Lesson 1 The Basics of Geometry

Lesson 1
The Basics of Geometry
Review Basic Algebra
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x + 4 = 16
2x – 11 = 3
(x – 1) . 10
(2 + 5) . 3 =
(12 + 1 – 9) ÷2 =
2x – 1 = 5
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Point
You can think of a point as a location. A point
has no size. It is represented by a small dot
and is named by a capital letter (example, • A).
Each point has a location described by two
numbers on Cartesian Plane.
What is Cartesian Plane?
Cartesian Coordinate Plane
A Cartesian Coordinate Plane consists of two
number lines that intersect. The horizontal
number line is called the x – axis and the
vertical number line is called the y – axis.
The point of intersection of the x – axis and y – axis is
called the ORIGIN
The axes divide the coordinate plane into four
quadrants.
Y axis
Quadrant II
Quadrant I
Origin
X axis
Quadrant III
Quadrant IV
Any point on the plane can be named by its x and y coordinates.
These coordinates are written as an Ordered Pair
(x, y). The x and/or y coordinate can be positive and/or negative
depending on which quadrant the point is in.
To determine the ordered pair of
a point you:
Read along the xaxis to identify the x
value. This is called
the x coordinate.
Read along the yaxis to identify the y
value. This is called
the y coordinate.
(0, 0)
Ex. 1 Plot each point in the Cartesian coordinate plane below.
A (4, -5)
B(1, 3)
C(-2, 4)
C
B
A
Ex. 2 Write the coordinates of the points below
and identify which quadrant each point is
B (5, 5) Quadrant I
located.
C (-5, 5) Quadrant II
D (-6, 2) Quadrant II
E (-6, -5) Quadrant III
F (0, -6) No Quadrant
G (6, -3) Quadrant IV
H (4, 0) No Quadrant
J (-4, -2) Quadrant III
K (1, -4) Quadrant IV
L (2, 2) Quadrant I
M (-2, 7) Quadrant II
N (-2, 3) Quadrant II
Shifting Vertically and Horizontally
Point Z(3,5)
Move 5 units to the left
Z
Move 7 units down
Label the new point as W
III
W is in quadrant ____
W