Quarter 1 Flashcards
He invented the rectangular coordinate system.
René Descartes
It is the system for graphic coordinates named after the French Mathematician René Descartes (1596–1650).
Rectangular Coordinate System
Another term for the rectangular coordinate system.
Cartesian Coordinate System
The horizontal line in a cartesian plane.
x-axis
The vertical line in a cartesian plane.
y-axis
The point of intersection of the axes.
Origin
The relationship between the two axes.
They are perpendicular to each other and divide the plane into four sections.
The four sections in the cartesian plane.
Quadrants
How are quadrants numbered?
Counterclockwise
Every point in the coordinate system can be described by ______________.
an ordered pair (x,y)
The first number in an ordered pair (x).
x-coordinate
Another term for x-coordinate.
Abscissa
What is an x-coordinate?
It determines the distance of the point from the origin measured along the x-axis. It is also the distance from a point to the vertical line or the y-axis.
The second number in an ordered pair (y).
y-coordinate
Another term for y-coordinate.
Ordinate
What is a y-coordinate?
It tells the distance from the origin measured along the
y − axis. It is also defined as the distance
from a point to a horizontal line.
The ordered pair that represents a point is called __________________.
coordinates of the point
____________________ is a branch of mathematics that deals with the algebraic procedures applied to geometry and where the position is represented analytically by coordinates.
Analytic/Coordinate Geometry
The ___________ between any two points in the plane is the
length of the line segment joining them.
distance
It is the distance formula.
d is equal to the square root of the sum of the square of the difference of xsub2 and xsub1 and ysub2 and ysub1
Distance is always ___________ regardless of the direction.
positive
___________________________ are defined only for pairs of points on a coordinate axis.
Directed distances
Directed distance may be ______________________.
positive or negative
The distance formula is derived from the _________________.
Pythagorean Theorem
It is the rate of change illustrated by the steepness of the line or ___________.
Slope
Vertical change in the line.
Rise
Horizontal change in the line.
Run
The formula in finding the slope.
m is equal to the quotient of the difference of ysub2 and ysub1 and xsub2 and xsub1
If xsub1 is equal to xsub2, L is a ___________ and m is _________.
vertical line; undefined/90 degrees
If ysub1 is equal to ysub2, L is a ___________ and m is _________.
horizontal line; zero
The trend of the line is upward from left to right.
Positive
The trend of the line is downward from left to right.
Negative
Points that lie on the same straight line are called _____________________.
Collinear Points
If points are collinear, the set of points will have the _______ slope.
same
The angle formed by the intersection of the x-axis and a nonhorizontal line determines the ____________________.
inclination of the line
The formula in finding the angle of inclination is derived from the ___________________.
tangent ratio
It is the formula in finding the angle of inclination.
theta is equal to arctan m
The gradient of a straight line is also the same as the ____________ of the angle formed between the line and the positive direction of the x − axis.
tangent
For horizontal lines, the angle of inclination is ___________.
0 or 180 degrees
The slope of the horizontal line is _________.
0
For vertical lines, the angle of inclination is ______.
90 degrees
The slope of the vertical line is _________.
undefined
It is the formula in finding the slope given the inclination of a line.
m is equal to tangent of theta
It is the formula in finding the angle between two lines.
tan theta is equal to the quotient of the difference of msub2 and msub1 and the sum of 1 and the product of msub1 and msub2
If tan theta is > 0, then the angle between the two lines is ________.
acute
If tan theta is < 0, then the angle between the two lines is ________.
obtuse
If tan theta is 0, then the two lines is are either ________.
coincidental or parallel
If tan theta is infinity, then the two lines is are ________.
perpendicular
Two segments having equal lengths are said to be __________ segments.
congruent
A point that bisects a segment or divides a segment into two (2) congruent segments, is called the __________ of a segment.
midpoint
Theorem of the Midpoint Formula
The abscissa of the midpoint of a line segment is half the
sum of the abscissas of the endpoints and the ordinate of the midpoint of a line segment is half
the sum of the ordinates of the endpoints of the given line segment.
It is the point of intersection of the three medians of a triangle
Centroid
Theorem of the Centroid Formula
The three median of a triangle at the point whose abscissa is
1/3 the sum of the abscissas of the vertices of the triangle and whose ordinate is 1/3 the sum of the ordinates of
the vertices.
The Division of Line Segment Formula
y is equal to the sum of the product of rsub2 and ysub1 and rsub1 and ysub2 over the sum of rsub1 and rsub2
A _______________ in two variables is an equation that can be written in the form, ax+by=c, where a, b, and c are any real number, and such that a and b cannot be both zero.
linear equation
Slope-Intercept Form
y=mx+b, when slope (m) and y-intercept (b) is given
Two-Point Form
y-ysub1 = (ysub2-ysub1/xsub2-xsub1)(x-xsub1), when two points are given
Point-Slope Form
y-ysub1 = m(x-xsub1), when a point and slope (m) is given
Intercept Form
x/a + y/b = 1, when x (a) and y (b) intercepts are given
Lines in the same plane that do not intersect.
Parallel Lines
Lines that intersect, in which the intersection forms a right or 90-degree angle.
Perpendicular Lines
Lines are parallel when their slopes are ________.
same
Lines are perpendicular when their slopes are ______________________________.
different and reciprocal of each other
A _______________ is often used to represent the coefficients in a system of linear equations.
matrix
The ___________________ is a scalar value that can be computed
from the elements of a square matrix and encodes certain properties of the linear transformation
described by the matrix.
determinant
The determinant of a matrix A is denoted by det(A), det A, or
|A|.
determinant
Distance from a Line to a Point Formula
d = Axsub1+Bysub1+C / +or- sqr rt of A^2 + B^2
Distance from a Point to a Point Formula
d = |Csub1-Csub2| / +or- sqr rt of A^2 + B^2
