Distance Between
Two Lines on the
Coordinate Plane
Distance Formula
What is the Distance Formula?
The distance formula can be obtained by creating a
triangle and finding the length of the hypotenuse. The
hypotenuse of the triangle will be the distance between
the two points.
ex) What is the distance between the points (5, 6) and (– 12, 40) ?
Practice Problems
1.
Find the distance between the points (20, 16) and (15, 10).
click for answer :)
2. Find the distance between the points (55, 40) and (26, 18).
click for answer :)
3.
Find the distance between the points (-19, -18) and (-29, 21).
click for answer :)
Web Links
http://www.purplemath.com/modules/distform.ht
m
http://www.teacherschoice.com.au/maths_librar
y/analytical%20geometry/alg_15.htm
http://www.regentsprep.org/regents/math/geom
etry/GCG3/Ldistance.htm
Back to problems
Back to problems
Back to problems
Angles Formed with nonparallel lines and a transversal
Alexander Shepherd
Overview and explanation
•
1
3
5
2
4
7
6
Transveral
8
line 2
line 1
Angles adjacent to
each other are
supplements.
• Angles 1 & 7, 2 & 8
are consecutive
exterior angles
• Angles 3 & 5, 4 & 6
are consecutive
interior angles
Problems
• If angle 1 is a consecutive interior angle
to angle 3 which is an alternate interior
angle to angle 2, what is angle 2’s
supplement?
• If angle 4 and interior angle and is a
corresponding angle to angle 5 what
does it’s alternate exterior equal?
Links
• http://www.algebralab.org/lessons/lesso
n.aspx?file=Geometry_AnglesParallelLi
nesTransversals.xml
• http://library.thinkquest.org/2609/l2s4.ht
m
• http://library.thinkquest.org/20991/geo/p
arallel.html
Today’s Lesson: Simplify Radicals
Perfect Squares
4= 2x2
9= 3 x 3
16= 4 x 4
25= 5 x 5
36= 6 x 6
49= 7 x 7
64= 8 x 8
81= 9 x 9
100= 10 x 10
To simplify a radical: You will need to
know your perfect squares. This is
important for the first step to simplifying
radicals. To simplify a radical means to
find another expression with the same
value It does not mean to find a
decimal approximate
Steps to Simplifying Radicals
•
Step 1: Find the largest perfect square which will divide evenly into the number
under your radical sign. This means that when you divide, you get no
remainders, no decimals, no fractions.
•
Step 2: Write the number appearing under your radical as the product of the
perfect square and your answer from dividing.
•
Step 3: Give each number in the product its own radical sign.
•
Step 4: Reduce the "perfect" radical which you have now created.
•
Step 5: Then you reach your answer
Examples
48  16  3  16  3  4 3
3 50 = 3 25  2  3 25 2 = 3 5 2  15 2
18x y z  9  2  x  x  y  z  3x 2 y 2 2xz
5
4
4
4
Extra Help
• http://www.themathpage.com/alg/simplifyradicals.htm
• http://www.freemathhelp.com/Lessons/Algebr
a_1_Simplifying_Radicals_BB.htm
• http://www.nutshellmath.com/textbooks_gloss
ary_demos/demos_content/alg_simplifying_r
adicals.html
What is the law of
detachment?
By,
Steven Copertino
Law of Detachment
• The law of detachment is probably one
of the easiest topics in math.
• Basically, it states that if p=q is true,
then p and q are both true.
Still confused?
• Here’s some examples…
• "If it is sunny outside, I will hang out my
washing. " It is sunny outside. Therefore
we can say that I will hang out my
washing.
One more…
• “If it snows more
than four inches, we
will not have
school.” We got 2
feet of snow last
night. Therefore, we
do not have school.
• Good Job!
Slope Intercept Form
•It is probably one of the most frequently
used ways to express the equation of a
line.
•One goal is to be able to find the slope
of a line when you are given two
coordinates.
•We also are trying to find the yintercept.
Important Rules
• Formula for y intercept: y=mx+b
• M is the slope of the line and b is the y- intercept.
• When given two points of a line, the first thing you should find is
the slope. You would find it using the slope formula. y2 - y1
x2 - x1
• Then once you’ve found m, all you have to do is plug it into the y
intercept equation using an x and a y from one of the
coordinates that they give you.
Example Problems
1. (-2, 8) and (6, 12)
12 -8
6-2
4
12= 1(6)+b
b=6
Y= 1x+6
2. (0, 16) and (-8, 22)
22-16
6
-8 - 0 -8
16= 3/-4(0)+b
b=16
Y= 3/-4x+16
3. (2, 4) and (1, -2)
-2-4
m=6
1-2
4= 6(2)+b
b= -8
Y= -8x+b
4
m=1
m= 3/-4
Helpful Sites
• http://www.purplemath.com/modules/slopgrph.htm
• http://www.purplemath.com/modules/strtlneq.htm
• http://www.glencoe.com/sec/math/algebra/algebra1/al
gebra1_05/study_guide/pdfs/alg1_pssg_G041.pdf
What is logical reasoning?
Logical reasoning contains
contrapositive, converse, inverse
and conditional statements.
Conditional and Converse Statement
•
•
•
•
•
The contrapositive and conditional statement both have the same truth
value.
The conditional is not always true
Conditional- If the Jets win this Sunday, then they are going to the
super bowl.
Converse is- If the Jets are in the super bowl, then they won on
Sunday.
Converse and inverse have the same truth value.
Inverse and Contrapositive
Statements
• Inverse- make the conditional statement negative
Example-If the Jets don’t win on Sunday, then they
won’t be in the Super Bowl.
• Contrapositive- switch the hypothesis and
conclusion and negate both.
Example- If there not in the Super Bowl, then Jets
didn’t win on Sunday.
Helpful Links
• http://teacher.scholastic.com/maven/
• http://mathforum.org/pows/library/sets/fu
n_logic.html
• http://www.iqleap.com/logical-reasoning/
• You could also use your geometry
textbook for more practice!