Geometry Chapter 12 Flashcards
Collinear points
points which lie on the same straight line
If a line passes through the points P1(x1,y1) and P2(x2,y2), then
Slope of P1P2=
y2-y1
x2-x1
The distance between two points haveing the same y value is
the absolute value of the differences of their x values.
thus: The distance between P(6,1) and Q(9,1) is 9-6=3
The line whose equation is y=mx+b has
slope m
Using the trapezoid method can be used to find the area of a quadrilateral if
its verticies are given
lines that have the same slope are
parallel to each other
The locus of points such that the sum of the squares of the coordinates is a constant
whose center is the orgin.
The constant is the square of the radius and the equation of the circle is
x^2+y^2=r^2
Parallel lines have
the same slope
If one side of a triangle is parallel to either coordinate axis, to find the area
1/2bh can be used
To find an area: If no side of a triangle is parallel to either axis then either
The triangle can be enclosed in a rectangle whose sides are parallel to the axes
Trapezoids whose bases are parallel to the y axis can be formed by dropping perpendiculars to the x axis
The locus of points whose y value and x value are related by either of the equations
where m and b are constants, is a line
If a line is parallel to the x-axis,
its inclination is 0 and its slope is 0
The distance between the points P1(x1,y1) and P2(x2,y2) is
If a line is perpendicular to the x-axis
its inclination is 90degrees and it has no slope
Perpendicular lines have slopes that are
negative reciprocals of each other. (Negative reciprocals are numbers, such as 2/5 and -5/2 whose product is -1)
The locus of points whose y value equals the product of a constant m and its x value is a straight line passing through the orgin;
its equation is y=mx
The constant m is the slope of the line
The slope of a line equals
the tangent of its inclination
The distance between two points having the same x value is
the absolute value of the difference of their y value.
Thus: P(2,1) and Q(2,4) is 4-1=3
If a line slants downward from left to right
its inclination is an obtuse angle and its slope is negative
The locus of points whose x value is a constant k is a line parallel to the y-axis;
its equation is x=k
The locus of points whose y value is constant k is a line parallel to the x-axis;
its equation is y=k
If the slope of a segment between a first point and a second equals the slope of the segment between either point and a third,
then the points are collinear
If a line slants upward from left to right
its inclination i is an acute angle and its slope is positive
The slope of a straight line is
constant all along the line
