1.2THE EQUATION OF A LINE IS OFTEN WRITTEN IN SLOPE-INTERCEPT FORM WHI...
1
.2
The equation of a line is often written in slope-intercept form which is y= mx+ b,where mis the slopeand bis the y-intercept.Important Information about Slope
■
A line that rises to the right has a positive slope and a line that falls to the right has a negative slope.■
A horizontal line has a slope of 0 and a vertical line does not have a slope at all—it is undefined.■
Parallel lines have equal slopes.■
Perpendicular lines have slopes that are negative reciprocals.–
A C T M AT H T E S T P R A C T I C E
–
D
ISTANCE
The distance between two points can be found using the following formula:d= (x2
−x1
)2
+ (y2
−y1
)2
M
IDPOINT
The midpoint of two points can be found by taking the average of the xvalues and the average of the yvalues.x
2
y
2
,
y
1
+
)midpoint = (
x
1
+
C
ONICS
Circles, ellipses, parabolas, and hyperbolas are conic sections. The following are the equations for each conicsection.Circle: (x−h)2
+ (y−k)2
= r2
where (h, k) is the center and ris the radius.h)
2
k)
2
+
(y
−
= 1 where (h, k) is the center. If the larger denominatorEllipse:
(x
−
a
2
b
2
is under y,the y-axis is the major axis. If the largerdenominator is under the x-axis, the x-axis is themajor axis.Parabola y−k= a(x−h)2
or x−h= a(y−k)2
The vertex is (h, k). Parabolas of the first form openup or down. Parabolas of the second form open leftor right.x
2
y
2
Hyperbolaa
2
−
b
2
= 1 ora
2
−b
2
= 1Plane GeometryPlane geometry covers relationships and properties of plane figures such as triangles, rectangles, circles, trape-zoids, and parallelograms. Angle relations, line relations, proof techniques, volume and surface area, andtranslations, rotations, and reflections are all covered in this section.To begin this section, it is helpful to become familiar with the vocabulary used in geometry. The listbelow defines some of the main geometrical terms:Arc part of a circumferenceArea the space inside a 2 dimensional figureBisect to cut in 2 equal partsCircumference the distance around a circleChord a line segment that goes through a circle, with its endpoint on the circleDiameter a chord that goes directly through the center of a circle—the longest lineyou can draw in a circleEquidistant exactly in the middleHypotenuse the longest leg of a right triangle, always opposite the right angleParallel lines in the same plane that will never intersectPerimeter the distance around a figurePerpendicular 2 lines that intersect to form 90-degree anglesQuadrilateral any four-sided figureRadius a line from the center of a circle to a point on the circle (half of thediameter)Volume the space inside a 3-dimensional figureBASIC FORMULAS
Perimeter the sum of all the sides of a figureArea of a rectangle A= bhh
Area of a triangle A=
b
Area of a parallelogram A= bhArea of a circle A= πr2
Volume of a rectangular solid V= lwhB
ASIC
G
EOMETRIC
F
ACTS
The sum of the angles in a triangle is 180°.A circle has a total of 360°.P
YTHAGOREAN
T
HEOREM
The Pythagorean theoremis an important tool for working with right triangles.It states:a2
+ b2
= c2
, where aand brepresent the legs and crepresents the hypotenuse.This theorem allows you to find the length of any side as along as you know the measure of the othertwo. So, if leg a = 1 and leg b = 2 in the triangle below, you can find the measure of leg c.acba2
+ b2
= c2
12
+ 22
= c2
1 + 4 = c2
5 = c2
5= cP
YTHAGOREAN
T
RIPLES
In a Pythagorean triple, the square of the largest number equals the sum of the squares of the other twonumbers.Example
As demonstrated: 12
+ 22
= (5)2