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ANALYTIC GEOMETRY > Quarter 1 > Flashcards

Quarter 1 Flashcards

1
Q

He invented the rectangular coordinate system.

A

René Descartes

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2
Q

It is the system for graphic coordinates named after the French Mathematician René Descartes (1596–1650).

A

Rectangular Coordinate System

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3
Q

Another term for the rectangular coordinate system.

A

Cartesian Coordinate System

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4
Q

The horizontal line in a cartesian plane.

A

x-axis

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5
Q

The vertical line in a cartesian plane.

A

y-axis

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6
Q

The point of intersection of the axes.

A

Origin

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7
Q

The relationship between the two axes.

A

They are perpendicular to each other and divide the plane into four sections.

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8
Q

The four sections in the cartesian plane.

A

Quadrants

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9
Q

How are quadrants numbered?

A

Counterclockwise

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10
Q

Every point in the coordinate system can be described by ______________.

A

an ordered pair (x,y)

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11
Q

The first number in an ordered pair (x).

A

x-coordinate

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12
Q

Another term for x-coordinate.

A

Abscissa

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13
Q

What is an x-coordinate?

A

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.

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14
Q

The second number in an ordered pair (y).

A

y-coordinate

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15
Q

Another term for y-coordinate.

A

Ordinate

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16
Q

What is a y-coordinate?

A

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.

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17
Q

The ordered pair that represents a point is called __________________.

A

coordinates of the point

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18
Q

____________________ is a branch of mathematics that deals with the algebraic procedures applied to geometry and where the position is represented analytically by coordinates.

A

Analytic/Coordinate Geometry

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19
Q

The ___________ between any two points in the plane is the
length of the line segment joining them.

A

distance

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20
Q

It is the distance formula.

A

d is equal to the square root of the sum of the square of the difference of xsub2 and xsub1 and ysub2 and ysub1

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21
Q

Distance is always ___________ regardless of the direction.

A

positive

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22
Q

___________________________ are defined only for pairs of points on a coordinate axis.

A

Directed distances

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23
Q

Directed distance may be ______________________.

A

positive or negative

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24
Q

The distance formula is derived from the _________________.

A

Pythagorean Theorem

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25
Q

It is the rate of change illustrated by the steepness of the line or ___________.

A

Slope

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26
Q

Vertical change in the line.

A

Rise

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27
Q

Horizontal change in the line.

A

Run

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28
Q

The formula in finding the slope.

A

m is equal to the quotient of the difference of ysub2 and ysub1 and xsub2 and xsub1

29
Q

If xsub1 is equal to xsub2, L is a ___________ and m is _________.

A

vertical line; undefined/90 degrees

30
Q

If ysub1 is equal to ysub2, L is a ___________ and m is _________.

A

horizontal line; zero

31
Q

The trend of the line is upward from left to right.

A

Positive

32
Q

The trend of the line is downward from left to right.

A

Negative

33
Q

Points that lie on the same straight line are called _____________________.

A

Collinear Points

34
Q

If points are collinear, the set of points will have the _______ slope.

A

same

35
Q

The angle formed by the intersection of the x-axis and a nonhorizontal line determines the ____________________.

A

inclination of the line

36
Q

The formula in finding the angle of inclination is derived from the ___________________.

A

tangent ratio

37
Q

It is the formula in finding the angle of inclination.

A

theta is equal to arctan m

37
Q

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.

A

tangent

38
Q

For horizontal lines, the angle of inclination is ___________.

A

0 or 180 degrees

39
Q

The slope of the horizontal line is _________.

A

0

40
Q

For vertical lines, the angle of inclination is ______.

A

90 degrees

41
Q

The slope of the vertical line is _________.

A

undefined

42
Q

It is the formula in finding the slope given the inclination of a line.

A

m is equal to tangent of theta

43
Q

It is the formula in finding the angle between two lines.

A

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

44
Q

If tan theta is > 0, then the angle between the two lines is ________.

A

acute

45
Q

If tan theta is < 0, then the angle between the two lines is ________.

A

obtuse

46
Q

If tan theta is 0, then the two lines is are either ________.

A

coincidental or parallel

47
Q

If tan theta is infinity, then the two lines is are ________.

A

perpendicular

48
Q

Two segments having equal lengths are said to be __________ segments.

A

congruent

49
Q

A point that bisects a segment or divides a segment into two (2) congruent segments, is called the __________ of a segment.

A

midpoint

50
Q

Theorem of the Midpoint Formula

A

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.

51
Q

It is the point of intersection of the three medians of a triangle

A

Centroid

52
Q

Theorem of the Centroid Formula

A

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.

53
Q

The Division of Line Segment Formula

A

y is equal to the sum of the product of rsub2 and ysub1 and rsub1 and ysub2 over the sum of rsub1 and rsub2

54
Q

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.

A

linear equation

55
Q

Slope-Intercept Form

A

y=mx+b, when slope (m) and y-intercept (b) is given

56
Q

Two-Point Form

A

y-ysub1 = (ysub2-ysub1/xsub2-xsub1)(x-xsub1), when two points are given

57
Q

Point-Slope Form

A

y-ysub1 = m(x-xsub1), when a point and slope (m) is given

58
Q

Intercept Form

A

x/a + y/b = 1, when x (a) and y (b) intercepts are given

59
Q

Lines in the same plane that do not intersect.

A

Parallel Lines

60
Q

Lines that intersect, in which the intersection forms a right or 90-degree angle.

A

Perpendicular Lines

61
Q

Lines are parallel when their slopes are ________.

A

same

62
Q

Lines are perpendicular when their slopes are ______________________________.

A

different and reciprocal of each other

63
Q

A _______________ is often used to represent the coefficients in a system of linear equations.

A

matrix

64
Q

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.

A

determinant

65
Q

The determinant of a matrix A is denoted by det(A), det A, or
|A|.

A

determinant

66
Q

Distance from a Line to a Point Formula

A

d = Axsub1+Bysub1+C / +or- sqr rt of A^2 + B^2

67
Q

Distance from a Point to a Point Formula

A

d = |Csub1-Csub2| / +or- sqr rt of A^2 + B^2

ANALYTIC GEOMETRY (1 decks)

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