ACE- Geometry 1119 Personal Handbook
equation of a circle whose center is not the origin
(x-h)²+(y-k)²=r²
midpoint formula
(x₁+x₂)/2, (y₁+y₂)/2
Theorem 105
A horizontal line has a slope of p,and a vertical line has no slope
Theorem 104
All segments on a nonvertical line have the same slope
Theorem 111
If the product of the slopes of two nonvertical lines -1,then they are perpendicular
Theorem 108
If two nonvertical lines are parallel then they have equal slopes
Theorem 110
If two nonvertical lines are perpendicular,then the product of their slope is -1
Theorem 109
If two nonvertical lines have equal slopes,then they are parallel
Theorem 113
The equation of a circle whose center is (h,k)and whose radius is r is (x-h)²+(y-k)=r²
Theorem 112
The equation of a circle whose center is at the origin with radius r is x²+y²=r²
Theorem 107
The equation of the line passing through the point (x₁,y₁)and having slope m is y-y₁=m(x-x₁)
Theorem 102
The formula for the distance ,d,between two points (x₁,y₁) and (x₂,y₂) is d=√(x₂-x₁)² + (y₂-y₁)²(Distance Formula Theorem)
Theorem 106
The graph of an equation in the form Ax+By=C,with both A and B not equal to zero is a line
Theorem 103
The midpoint of the segment joining the points (x₁,y₁)and (x₂,y₂) (Midpoint Formula Theorem)
coordinates
an ordered pair of numbers which indicate the location of a point on a coordinate plane
Distance Formula
d = √( x₂ - x₁)² + (y₂ - y₁)²
absolute value
for any pair of opposite, the positive number
y-intercept
is the y-coordinate of the point where the graph of a line crosses the y-axis
slope
m=y₂-y₁/x₂-x₁
|a|
the absolute value of a
abcissa
the first number of an ordered pair
quadrants
the four regions of the coordinate plane formed by the two axes
x-axis
the horizontal axis
origin
the point of intersection of these two axes
slope
the slant of a line
y-axis
the vertical axis
ordinate
the y-coordinate,or second number
axes
two perpendicular lines
coordinate plane
when two number lines are perpendicular
equation of a circle whose center is the origin
x²+y²=r²
point slope form
y - y₁ = m(x - x₁)
Two point equation
y-y₁= y₂-y₁/x₂-x₁ (x-x₁)
slope-intercept form
y=mx+b
