anonymous
  • anonymous
Question down below please I need help!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
freckles
  • freckles
what trouble are you having?
freckles
  • freckles
identifying the coordinates for C and D?

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anonymous
  • anonymous
Yes I don't know how to solve the problem overall
freckles
  • freckles
|dw:1437368521661:dw| y=b is a horizontal line any point falling on it will have it's y coordinate as b y=0 is a horizontal line any point falling on it will have it's y coordinate as 0
freckles
  • freckles
|dw:1437368652986:dw| what I'm saying is I know 2a comes after a sometime you could have picked something else I'm sure calling it x=c would have been fine we would just assume c>a
freckles
  • freckles
anyways x=a is a vertical line any point falling on it will have it's x coordinate as a x=2a is a vertical line any point falling on it will have it's x coordinate as 2a
freckles
  • freckles
so what coordinates are you going to assign to C?
freckles
  • freckles
notice the lines goes through point C above on the picture are x=2a and y=b and I did say any point on x=2a will have x-coordinate 2a and I also said any point on y=b will have y-coordinate b so we could give the coordinates of C as?
anonymous
  • anonymous
2a?
anonymous
  • anonymous
c has cordinates of 2a, b?
freckles
  • freckles
yes C has coordinate (2a,b) or that is what we are assigning C anyways it is appropriate since 2a does come after a but as I said before we could have pick another number like c and make the assumption c is greater than a but anyways |dw:1437369322715:dw| now we have to assign coordinates to D
freckles
  • freckles
notice D lays on the horizontal line y=0 any point falling on y=0 has y-coordinate 0
freckles
  • freckles
|dw:1437369388989:dw| what number are you going to put in place of that ?
anonymous
  • anonymous
umm 2a squared
freckles
  • freckles
I guess you could say 2a^2 the spacing between B's x-coordinate and C's x-coordinate seem pretty close to the spacing between C's x-coordinate and D's x-coordinate I think a better number might be 3a but I think 2a^2 would be great if we don't care about scales
freckles
  • freckles
by the way that is according to your picture I have drawn my D a little closer to my C than the pic actually shows
freckles
  • freckles
|dw:1437369720333:dw|
anonymous
  • anonymous
ok
freckles
  • freckles
now we want to verify that is a trapezoid
freckles
  • freckles
So we need to show the slope of line segment BC is the same as the slope of the line segment AD
freckles
  • freckles
This is because a trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides that are parallel. To show two lines are parallel you just show that their slopes are equal.
freckles
  • freckles
\[\text{ slope of a line } y=mx+b \text{ with coordinates } (x_1,y_1) \text{ and } (x_2,y_2) \\ \text{ is } \frac{y_2-y_1}{x_2-x_1}\]
freckles
  • freckles
so line BC has points (a,b) and (2a,b) so it's slope is?
anonymous
  • anonymous
I don't know actually.
freckles
  • freckles
you can also just observe from the picture the slope of line segment BC is zero since it is a horizontal line segment but you can also do it algebraically using the formula I gave you have: \[(x_1,y_1)=(a,b) \text{ and } (x_2,y_2)=(2a,b) \\ \text{ so } x_1=a \\ y_1=b \\ x_2 =2a \\ y_2=b \\ \text{ so entering into the the formula } \\ \frac{y_2-y_1}{x_2-x_1}=\frac{b-b}{2a-a}\] we know that b-b=0 and 2a-a=a and 0/a is 0 (since we also know a is not 0)
anonymous
  • anonymous
oh ok
freckles
  • freckles
anyways we also need the slope of the side that is opposite to BC
freckles
  • freckles
if we can show that the side opposite to BC has the same slope I would say we are done since obviously the shape is 4-sided flat shape
freckles
  • freckles
What did I say the slope of any horizontal line is?
anonymous
  • anonymous
0?
freckles
  • freckles
so slope of BC is 0 and slope of AD is 0 |dw:1437370464744:dw| the opposite sides called BC and AD are parallel since they both have the same slope I think they asked you to find the coordinates to use the slope formula though (but honestly that is kind of weird since the line segments BC and AD obviously appear horizontal ) \[\text{ slope of } BC=\frac{b-b}{2a-a}=\frac{0}{a}=0 \\ \\ \text{ slope of } AC=\frac{0-0}{3a-0}=...\] I will let you finish that if you want to.
freckles
  • freckles
anyways that is done we have shown this 4-sided flat shape does consist of opposite sides that are parallel
anonymous
  • anonymous
0/3a
freckles
  • freckles
and 0/(3a) is 0 since 0/anything =0 (exlcuding the anything from being 0) (we know a isn't 0 since according to the picture a is greater than 0)
freckles
  • freckles
in short 0/(3a)=0
anonymous
  • anonymous
thank you
freckles
  • freckles
np do you have anymore question about this question?
freckles
  • freckles
I'm about to vanish into thin air
anonymous
  • anonymous
no thank you though
freckles
  • freckles
abracadabra

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