## anonymous one year ago Question down below please I need help!!

1. anonymous

2. freckles

what trouble are you having?

3. freckles

identifying the coordinates for C and D?

4. anonymous

Yes I don't know how to solve the problem overall

5. 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

6. 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

7. 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

8. freckles

so what coordinates are you going to assign to C?

9. 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?

10. anonymous

2a?

11. anonymous

c has cordinates of 2a, b?

12. 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

13. freckles

notice D lays on the horizontal line y=0 any point falling on y=0 has y-coordinate 0

14. freckles

|dw:1437369388989:dw| what number are you going to put in place of that ?

15. anonymous

umm 2a squared

16. 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

17. 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

18. freckles

|dw:1437369720333:dw|

19. anonymous

ok

20. freckles

now we want to verify that is a trapezoid

21. freckles

So we need to show the slope of line segment BC is the same as the slope of the line segment AD

22. 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.

23. freckles

$\text{ slope of a line } y=mx+b \text{ with coordinates } (x_1,y_1) \text{ and } (x_2,y_2) \\ \text{ is } \frac{y_2-y_1}{x_2-x_1}$

24. freckles

so line BC has points (a,b) and (2a,b) so it's slope is?

25. anonymous

I don't know actually.

26. 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)

27. anonymous

oh ok

28. freckles

anyways we also need the slope of the side that is opposite to BC

29. 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

30. freckles

What did I say the slope of any horizontal line is?

31. anonymous

0?

32. 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.

33. freckles

anyways that is done we have shown this 4-sided flat shape does consist of opposite sides that are parallel

34. anonymous

0/3a

35. 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)

36. freckles

in short 0/(3a)=0

37. anonymous

thank you

38. freckles

39. freckles

I'm about to vanish into thin air

40. anonymous

no thank you though

41. freckles