Coordinate Geometry & Lines

Question 1

Distance Formula

Answer 1

The distance between the points P1(x1, y1) and p2(x2, y2) is

|P1P2| = _/(x2-x1)^2 + (y2-y1)^2

Question 2

Line Definition

Answer 2

The Slope of a nonvertical line that passes through the points P1(x1, y1) and P2(x2,y2) is

m = y2 - y1 / x2 - x1

A vertical line is not defined

Question 3

Point-Slope Form of The Equation of a Line

Answer 3

An equation of a line passing through the point P1(x1,y1) and having slope m is

y - y1 = m(x-x1)

Question 4

Slope-Intercept Form of the Equation of a Line

Answer 4

An equation of the line with slope m and y-intercept b is

y = mx + b

Question 5

Every Equation of Every Line can be written in the form

Answer 5

Ax + By + C = 0

Question 6

Parallel and Perpendicular Lines

Answer 6

1. Two nonvertical lines are parallel if and only if they have the same slope.
2. Two Lines With Slopes M1 and M2 are perpendicular if and only if m1m2 = -1; thast is, their slopes are negative reciprocals

m2 = -1/m1

Question 7

Equation of a Circle

Answer 7

An equation of a circle with the center (h, k) and radius r is

(x-h)^ 2 + (y - k)^ 2 = r^ 2

IF the center is the origin (0, 0) the equation is

x^ 2 + y^ 2 = r^ 2

Question 8

Parabolas

Answer 8

As a graph of an equation of the form

y = ax^ 2 + bx + c

Question 9

Ellipses

The Curve With Equation

Answer 9

x^ 2 / a^ 2 + y^ 2 / b^ 2 = 1

Question 10

Hyberolas

The Curve WIth Equation

Answer 10

x^ 2 / a^ 2 - y^ 2 / b^ 2 = 1

Question 11

Shifted Conics

Answer 11

If the center point is the point (h, k) then the equation of the circle becomes

(x - h)^ 2 / a^ 2 + (y - k)^ 2 / b^ 2 = 1

Question 12

Trigonometric Functions

Answer 12

Sin = O/H
Cos = A/H
TAN = 0/A
CSC = H/O
SEC = H/A
COT = A/O

Question 13

Trigonometric Functions for Obtuse Angles

Answer 13

SIN = Y/R
COS = X/R 
TAN = Y/X
CSC = R/Y
SEC = R/X
COT = X/Y 

X = POINT
Y = POINT
R = DISTANCE

Question 14

Trigonometric Identities

Answer 14

CSC = 1/SIN
TAN = SIN/COS
SEC = 1/COS
COT = COS/SIN
COT? = 1/TAN

Question 15

Trigonometric Identities

Addition Formulaas

Answer 15

sin(x+y) = sin x cos y + cos x sin y

cos(x+y) = cos x cos y - sin x sin y

tan(x+y) = tan x + tan y / 1 - tan x tan y

Question 16

Trigonometric Identities

Subtraction Formulaas

Answer 16

sin(x-y) = sin x cos y - cos x sin y

cos(x-y) = cos x cos y + sin x sin y

tan(x-y) = tan x - tan y / 1 + tan x tan y

Question 17

Trigonometric Identities

Double-Angle Formulaas

Answer 17

sin 2x = 2 sin x cos x

cos 2x = cos^ 2 x - sin^ 2 x

cos 2x = 2 cos^ 2 x - 1

cos 2x = 1 - 2 sin^ 2x

Question 18

Trigonometric Identities

Half-Angle Formulaas

Answer 18

cos^ 2 x = 1 + cos2 x / 2

sin^ 2x = 1 - cos 2 x / 2

Question 19

Trigonometric Identities

Product Formulaas

Answer 19

sin x cos y = 1/2[sin(x + y) + sin(x - y)]

cos x cos y = 1/2 [ cos ( x + y) + cos ( x - y)]

sin x sin y = 1/2 [ cos (x - y) - cos (x + y)]

Question 20

4 Ways to Represent a Function

Answer 20

Verbally
Numerically
Visually
Algebraically

Question 21

Vertical Line Test

Answer 21

A curve in the xy plane is the graph of a function of x if and only if no vertical line intersects the curve more than once.

Question 22

Piecewise Defined Functions

Answer 22

Defined by
f(x) = {1 - x if x /< - 1
{x^ 2 if x > -1

Question 23

Symmetry

Even

Answer 23

If a function satisfies f (-x) = f (x) for every number x in its domain, then f is called an even function

Question 24

Symmetry

Odd

Answer 24

If satisfies f (-x) = -f(x) for every number x in its domain, then f is called an odd function

Question 25

A function f is called decreasing if

Answer 25

f(x1) > f(x2) whenever x1 < x2 in I

Question 26

A function f is called increasing if

Answer 26

f(x1) < f(x2) whenever x1 < x2 in I