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**rogerwaters**- Replies: 4

Hi, I need help with this transformation lesson. I'll post 5 at a time.

1. An angle changes in size as it undergoes a dilation.

A False

B True

2. A line segment usually decreases in size under contraction.

A False

B True

3. There can only be one obtuse angle in a triangle.

A False

B True

4. If a figure is reflected across the x-axis it is congruent to the original figure.

A False

B True

5. A figure derived from a previous figure by rotation, translation or dilation will be congruent to the original figure.

A False

B True

Okay I sent in the previous lesson and I'm awaiting for the teacher's response.

Meanwhile I figured out the first 10 from the next lesson but need help with the second 10. The lesson is "The Cartesian Coordinate System and the Distance Formula" I'll wait for you to wake up and reply. Thanks again for the previous lesson!

Find the distance between the two points:

11. (-20, -4) and (-7, -6)

A 4

B SQRT(61)

C SQRT(290)

D 5

E SQRT(173)

F SQRT(180)

12. (1, 1) and (-4, 1)

A 4

B SQRT(61)

C SQRT(290)

D 5

E SQRT(173)

F SQRT(180)

13. (-3, 22) and (-14, 35)

A 4

B SQRT(61)

C SQRT(290)

D 5

E SQRT(173)

F SQRT(180)

14. (9, -0) and (-3, -8)

A 4

B SQRT(61)

C SQRT(290)

D 4[SQRT(13)]

E 5[SQRT(17)]

F 3[SQRT(180)]

15. (1, 2) and (5, 2)

A 4[SQRT(13)]

B SQRT(61)

C SQRT(29)

D SQRT(202)

E 4

F SQRT(60)

What is the radius of a circle with the given center C that passes through the given point Z?

16. C (0, 0); Z (-8, 0)

A 4

B SQRT(61)

C 8

D 5

E SQRT(173)

F SQRT(180)

17. C (-4, -5); Z (-10, -5)

A 4

B SQRT(202)

C SQRT(290)

D SQRT(61)

E SQRT(173)

F 6

18. C (-5, 8); Z (-5, 4)

A 4

B SQRT(61)

C SQRT(290)

D SQRT(202)

E SQRT(173)

F 6

19. C (-5, 9); Z (6, 0)

A 4

B SQRT(61)

C SQRT(290)

D SQRT(202)

E SQRT(173)

F SQRT(180)

20. C (-7, 6); Z (-13, -6)

A 4

B SQRT(202)

C SQRT(290)

D SQRT(61)

E SQRT(173)

F SQRT(180)

Never mind! I got them all and sent them in and got 20/20!

Alright I'll try those. Are you sure they are correct?

Okay that's the area. What about the volume.

Can you write formula and solve it in step WRITTEN DOWN

So I could copy it.

I have no idea. Math is my weakest subject and I'm really confused

I have no idea what's going on.

b is (1/2) of 10.75 = 5.375 inches

May I ask how you got 10.75 inches?

Alright, but what are 'a' and 'b' equal to?

Alright now here's the really tough one, it's worth 4 points.

7. Problem solver (worth 4 points): Come up with a way to find the area and volume of a football. Include in your answer a way to acquire any necessary measurements without cutting or otherwise destroying the football. Also include all necessary formulas to implement your idea. (You don't need to find actual numbers, just outline the method in step by step detail--think of all the measurements you'll need to acquire and how you'll get them.)

a = 9^2 x 6 * tan x (180/6)

a = 280.59

And what about 6?

What is the easier way?

Alright! Could you check 4 for me?

And here are my answers for number 5 and 6?

5. If a hexagon is resting on a flat side, and has a total height of 18, what is the length of each side of the hexagon?

A = 9^2 x 6 * tan x (180/6)

A = 280.59

Now that I have the area, I have to find the side where s = side of the hexagon.

3 (√3 /2) x S^2 = 280.59

s^2 = 280.59 x 2 / 3 x √3

s^2 = 561.18 / 5.196152

s^2 = 107.99

s = 10.39

a = 9^2 x 6 * tan x (180/6)

a = 280.59

Oh oh!!! If the radius is 6, then the side is equal 6 right?

So that is my answer: If the radius is equal to 6, then the side is equal to 6 as well.

I also got number 4:

4. If a hexagon has a radius (center to point of angle) of 6, what is the area of the hexagon?

First we find the area of one triangle:

area(t) = r^2 sqrt3 /4

area(t) = 6^2 sqrt3 /4

area(t) = 36 x sqrt3 /4

area(t) = 36 x .433021

area(t) = 15.588756

area(h) = 6 x 15.588756

area(h) = 93.53

But the given only tells me that the radius is 6, how did you get the side?

I'm really confused

That's for number 3 right?

I did not submit it. I need to find all of the answers first.

You might wanna check that!

What formula did you use?

Alright thanks! So let's move to number 3

After that, we'll move on to number 3

1. If a hexagon has a side of 3 units, what is the area of the hexagon?

area = 3^2 x 6 / 4 x tan(180/6)

area = 54 / 4 x tan(180/6)

area = 54 / 2.3094

area = 23.38

or

area = 1/2 (3sqrt3) * s^2

area = 1/2 (3sqrt3) * 3^2

area = 1/2 (3sqrt3) * 9

area = 23.38

2. If a hexagon has an area of 100 units, what is the length of one side?

100= 3√3 / 2 * s² | s = side

s^2 = 100 / 3√3 / 2

s^2 = 100 / 2.598076

s^2 = 38.490021

Answer: s = 6.204032

But the formula you recommended does not lead to the same result.

So

1. area = 1/2 (3sqrt3) * s^2

area = 1/2 (3sqrt3) * 3^2

area = 1/2 (3sqrt3) * 9

What next?

I looked up a little bit online and found out that this formula should be used

s^2 x 6 / 4 x tan(180/6)

Is that also correct?