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.htm

http://www.teacherschoice.com.au/maths_library/analytical%20geometry/alg_15.htm

http://www.regentsprep.org/regents/math/geometry/GCG3/Ldistance.htm

Back to problems

Back to problems

Back to problems

Angles Formed with non-parallel lines and a transversal

Alexander Shepherd

Overview and explanation

• 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

line 1

line 2

Transveral

∠5 ∠7∠6 ∠8

∠1 ∠3

∠2 ∠4

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/lesson.aspx?file=Geometry_AnglesParallelLinesTransversals.xml

• http://library.thinkquest.org/2609/l2s4.htm

• http://library.thinkquest.org/20991/geo/parallel.html

Today’s Lesson: Simplify Radicals

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

Perfect Squares4 = 2 x 29= 3 x 316= 4 x 425= 5 x 536= 6 x 649= 7 x 764= 8 x 8 81= 9 x 9 100= 10 x 10

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

18x5 y4z = 9 • 2 • x4 • x • y4

• z =3x2y2 2xz

Extra Help

• http://www.themathpage.com/alg/simplify-radicals.htm

• http://www.freemathhelp.com/Lessons/Algebra_1_Simplifying_Radicals_BB.htm

• http://www.nutshellmath.com/textbooks_glossary_demos/demos_content/alg_simplifying_radicals.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 y- intercept.

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 Problems1. (-2, 8) and (6, 12) 12 -8 4 m=1 6 - 2 412= 1(6)+b b=6Y= 1x+6

2. (0, 16) and (-8, 22) 22-16 6 m= 3/-4

-8 - 0 -816= 3/-4(0)+b b=16Y= 3/-4x+163. (2, 4) and (1, -2) -2-4 m=6 1-2 4= 6(2)+b b= -8Y= -8x+b

Helpful Sites

• http://www.purplemath.com/modules/slopgrph.htm

• http://www.purplemath.com/modules/strtlneq.htm

• http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_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/fun_logic.html

• http://www.iqleap.com/logical-reasoning/

• You could also use your geometry textbook for more practice!