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plot the points A= (5,3), B= (-4, -6) and D =(5,-6) on a set of axes. use a ruler to connect them inorder , including D back to A, to form a QUADRILATERAL ( a shape with four sides ) A) what kind of quadrilateral was formed? B) how long is each side of quadrilateral? C) what is the area of the quadrilateral? D) what is the perminitor?
i think we need point C
A= (5,3) B = (-4,3) C= (-4,-6) D= (5,-6)
do you notice any straight lines, vertically and horizontally
well idont have any graph paper
_ o - o - - | | | - | | | | - - o - o does that give you idea of what it looks like
noo ihavent done the problem because idont have any graph paper but can we try another problem ?
you dont need graph paper, make your own graph if you connect those points above what shape does it look like?
oh okae kool ill try it out right now and see what igot ..
its a square right ?
yes good job now count how long is each side?
what do u mean count how long is each side? how do i count it ?
one of the quadrilateral tht was formed is a square right ?
when you made your graph, you had to use marks along the axis to make your points count how many marks it takes to get from one point to the next
igot 41 ?
wait 41 points is the perimiter right ?
lets try something different look at point A and B
each side is 10 points
yes i think you kept counting all the way around
A is (5,3) B is (-4,3) Notice the 3 stayed the same how much changed for the x-value from -4 to 5
yeah thats what iwas doing but from A to B is 10 points .
oh dont include the first point count the spaces
so its 8 points ?
no. count the spaces in between the tick marks
yeah igot it is 8 points .
okay thats not right. let's try a different way. look at the x-coordinates for A and B. which is A = 5 and B = -4. then add those numbers together (don't bother with the negative sign. just ignore it). what do you get when you add them together.
9 im very confused about this
u said it was -4 thats why igot 1
i know. but i also said to ignore the negative sign. when dealing in distances you don't deal with negative numbers that's why you can ignore the negative sign and treat the number like a positive number. do you understand this?
yeah now idoo . so its 9 points to get across to another point?
| - - - -| - - - - - | here is a visual how many dashes on either side
yes. it's 9 points. now lets figure out the perimeter. how would you go about figuring this out?
iget it now ... its going to be 9 times 4?
yes. good job.
we skipped question C
do you know the formula for area?
okay. area = length x width (A= lw) what is the length and width?
idont get it?
okay. length refers to number of points from A to B or C to D. width refers to the number of points from A to D or B to C.
so what does length equal and width equal?
youu add them all up ?
or u multiply them ?
okay. remember before when you found that all the distances from each point are 9. that's why the perimeter is 4 x 9. because there are 4 sides and each side has the distance of 9. so when finding area all you need to do is take the distance from one side and multiply it by another side. you with me?
not really im confused
9 times 9?
yes. do you want me to try to explain the area formula?
can u help me with more problems please?
okay. here's a sample problem: find the area of the rectangle. ____________ | | | | 5 |___________| 7 the area formula is A=lw A=Area l = length w = width so the find the area of the above rectangle you need to do what first?
sorry the rectangle got messed up a bit
35 ? kus u times 5 and 7
yes. good job :) the length is 7 the width is 5 do you have another problem that you want to solve?
yes . A) draw a rectangle using Algebra tiles with area 2x + 4. write an algebraic expression for the dimensions of the rectangle formed with the tiles. B) draw a rectangle using Algebra tiles with area 2x^2 + 4x in two different ways. write the algebraic expression for each rectangle. C) how are the sketches for parts (a) and (b) different?
A) okay this would help if you draw a rectangle (don't worry about the dimensions we'll figure that out later).
_______________ | | | | ------------- something like this. now we'll need to use the area formula to figure out the dimensions. can you tell me what the area formula is?
15 times 2?
the rectangle i drew is just a visual aid. i'm asking for the area formula. whenever someone is asking for a math formula they don't want specific numbers but the general formula that uses letters that represent numbers. you with me?
yeah isnt it 2x+4?
for this specific problem the area does equal 2x + 4, however, i'm asking for the general area formula that applies to any area question. the area formula is A=lw. can you tell me what l and w mean?
the area formula is A=lw A=Area l = length w = width
yes. good job. now for this problem they gave you area. A = 2x + 4. so we know that also equals length time width A = lw A = 2x + 4 2x + 4 = lw you with me?
not really im confused
okay. do you know what substitution means?
what grade are you?
i need to know so i can explain this in terms that you will understand
are you taking algebra 1?
have you gone over factoring?
yes but idont get math at all
don't worry most people don't get it. it just takes practice. now can you factor anything out from 2x + 4?
you can factor something out from both terms. can you tell me what the greatest common factor is for 2x and 4?
think about it like this. 2x = (2)(1)(x) 4 = (2)(2) they both have in common a 2. so we can factor out the 2 so it looks like this: 2(1x + 2) make sense?
just a lil bit
okay let's do this in steps step 1: start with the original expression which in this case is 2x + 4 step 2: break the expression down into its factors: (2)(1)(x) + (2)(2) which still equals the original expression step 3: find the number that both terms have in common, which would be 2 step 4: factor out the 2 so it looks like this: 2(x+2) which still equals the original expression do you have any questions about this?
so you get it?
yeah iget what u explained to me just a lil idont get how to do the problems
okay remember the area formula is A=lw and the problem stated that the A=2x+4. we then factored the area into 2(x+2) which gives us 2 separate terms the problem is asking for the dimensions which is length and width A=lw A=2x+4 2x+4 = 2(x+2) A=2(x+2) 2(x+2) = lw you with me?
yeah so iwrite tht down for A
not quite. can you tell me what the length is?
no. the area is 2x+4. i'm asking for the length area formula: A=lw A=area l= length w=width
so u asked for the formula?
i'm sorry but i don't know how else to explain this so here are the answers A) draw a rectangle using Algebra tiles with area 2x + 4. write an algebraic expression for the dimensions of the rectangle formed with the tiles. answer: A = 2(x+2) A=2x+4 l = 2 w = x+2 B) draw a rectangle using Algebra tiles with area 2x^2 + 4x in two different ways. write the algebraic expression for each rectangle. answer: A = 2x^2 + 4x A = 2x(x+2) l = 2x w = x+2
thanks so much for ur help . what is C?
you need to sketch out the rectangles for a and b then you can figure out c. it's too difficult to do that on here. best wishes. bye.
thanks so much for all ur help!!!!!!!