Quarter 1

Question 1

He invented the rectangular coordinate system.

Answer 1

René Descartes

Question 2

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

Answer 2

Rectangular Coordinate System

Question 3

Another term for the rectangular coordinate system.

Answer 3

Cartesian Coordinate System

Question 4

The horizontal line in a cartesian plane.

Answer 4

x-axis

Question 5

The vertical line in a cartesian plane.

Answer 5

y-axis

Question 6

The point of intersection of the axes.

Answer 6

Origin

Question 7

The relationship between the two axes.

Answer 7

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

Question 8

The four sections in the cartesian plane.

Answer 8

Quadrants

Question 9

How are quadrants numbered?

Answer 9

Counterclockwise

Question 10

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

Answer 10

an ordered pair (x,y)

Question 11

The first number in an ordered pair (x).

Answer 11

x-coordinate

Question 12

Another term for x-coordinate.

Answer 12

Abscissa

Question 13

What is an x-coordinate?

Answer 13

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.

Question 14

The second number in an ordered pair (y).

Answer 14

y-coordinate

Question 15

Another term for y-coordinate.

Answer 15

Ordinate

Question 16

What is a y-coordinate?

Answer 16

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.

Question 17

The ordered pair that represents a point is called __________________.

Answer 17

coordinates of the point

Question 18

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

Answer 18

Analytic/Coordinate Geometry

Question 19

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

Answer 19

distance

Question 20

It is the distance formula.

Answer 20

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

Question 21

Distance is always ___________ regardless of the direction.

Answer 21

positive

Question 22

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

Answer 22

Directed distances

Question 23

Directed distance may be ______________________.

Answer 23

positive or negative

Question 24

The distance formula is derived from the _________________.

Answer 24

Pythagorean Theorem

Question 25

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

Answer 25

Slope

Question 26

Vertical change in the line.

Answer 26

Rise

Question 27

Horizontal change in the line.

Answer 27

Run

Question 28

The formula in finding the slope.

Answer 28

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

Question 29

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

Answer 29

vertical line; undefined/90 degrees

Question 30

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

Answer 30

horizontal line; zero

Question 31

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

Answer 31

Positive

Question 32

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

Answer 32

Negative

Question 33

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

Answer 33

Collinear Points

Question 34

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

Answer 34

same

Question 35

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

Answer 35

inclination of the line

Question 36

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

Answer 36

tangent ratio

Question 37

It is the formula in finding the angle of inclination.

Answer 37

theta is equal to arctan m

Question 37

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.

Answer 37

tangent

Question 38

For horizontal lines, the angle of inclination is ___________.

Answer 38

0 or 180 degrees

Question 39

The slope of the horizontal line is _________.

Answer 39

0

Question 40

For vertical lines, the angle of inclination is ______.

Answer 40

90 degrees

Question 41

The slope of the vertical line is _________.

Answer 41

undefined

Question 42

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

Answer 42

m is equal to tangent of theta

Question 43

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

Answer 43

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

Question 44

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

Answer 44

acute

Question 45

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

Answer 45

obtuse

Question 46

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

Answer 46

coincidental or parallel

Question 47

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

Answer 47

perpendicular

Question 48

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

Answer 48

congruent

Question 49

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

Answer 49

midpoint

Question 50

Theorem of the Midpoint Formula

Answer 50

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.

Question 51

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

Answer 51

Centroid

Question 52

Theorem of the Centroid Formula

Answer 52

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.

Question 53

The Division of Line Segment Formula

Answer 53

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

Question 54

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.

Answer 54

linear equation

Question 55

Slope-Intercept Form

Answer 55

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

Question 56

Two-Point Form

Answer 56

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

Question 57

Point-Slope Form

Answer 57

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

Question 58

Intercept Form

Answer 58

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

Question 59

Lines in the same plane that do not intersect.

Answer 59

Parallel Lines

Question 60

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

Answer 60

Perpendicular Lines

Question 61

Lines are parallel when their slopes are ________.

Answer 61

same

Question 62

Lines are perpendicular when their slopes are ______________________________.

Answer 62

different and reciprocal of each other

Question 63

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

Answer 63

matrix

Question 64

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.

Answer 64

determinant

Question 65

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

Answer 65

determinant

Question 66

Distance from a Line to a Point Formula

Answer 66

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

Question 67

Distance from a Point to a Point Formula

Answer 67

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