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Solve each equation. Leave answers as fractions.
1. 5x – 3 = 18
2. 4(x – 1) + 2 = 15
3. 8x + 9 = 14x – 3
4. 12x + 5 = 18x
5. 3(2x + 1) = 5(x + 7)
x = 21/5
x = 17/4
x = 2
x = 5/6
x = 32
Definition – A point represents one location in space. It has no size and NO DIMENSION.
AB
It represents the simplest form of geometry.
Notation: Points are named by capital letters.
Example: Points A and B
A series of points can create a line. A line extends in two directions without endpoints. A line has only one dimension.
Notation: Lines can be denoted by using two points that lie on the line or by using a lower case letter.
Given any two points, you can draw exactly one line. You can draw an infinite amount of lines through one point.
m
Line m
B
A
AB or BA
A two dimensional figure that extends in both dimensions forever and has no thickness.
Notation: A plane is either named by one capital letter (like a point) or by at least three points (but no more than four points) that lie in the plane.
Plane M
Plane ABC
or Plane ABCD
A C
BD
Where have you seen points, lines, and planes before in math class?
The Coordinate Plane
Graphing Lines in slope-intercept form. Ex. y = 2x + 2
Plotting Points. Ex. (-2, 4)
Collinear Points are points that lie on the same line.
A
B
CD
E
B, C, and D are noncollinear points.
A, C, and D are collinear points.
A
B
CD
E
Yes!! In fact any two points are collinear. We can always draw exactly
one line between two given points.
Are A and B collinear points?
Coplanar Points are points that lie on the same plane.
DB
A C
A, B, C, and D are coplanar points.
G HJ
K
K, J, G, and H are noncoplanar points.
The symbol for “to intersect” is We can find the intersection between sets of numbers.Example: Set A = {-2, 0, 2, 5, 6, 8}
Set B = {-3, -2, -1, 0, 6}
Find A B = {-2, 0, 6}
We can also find the Union of two sets. Find A B.
A B = {-3, -2, -1, 0, 2, 5, 6, 8}
Through any three points there is at least one plane. Through any three non-collinear points, there
is exactly one plane.
All collinear points are also coplanar.
However, coplanar points are not necessarily collinear.
A
BC
D