Dilation involves changing the size of a shape.
- See attachment for the graphs of ABC, A'B'C and A"B"C"
- A"B"C" is a dilation of A'B'C', with a scale factor of 1/4
From the given diagram, we have:
![\mathbf{A = (4,-2)}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%20%284%2C-2%29%7D)
![\mathbf{B = (-2,-2)}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%20%3D%20%28-2%2C-2%29%7D)
![\mathbf{C = (-2,2)}](https://tex.z-dn.net/?f=%5Cmathbf%7BC%20%3D%20%28-2%2C2%29%7D)
<u>(a) Dilate by scale factor 2 with center (0,0)</u>
We simply multiply the coordinates of ABC by 2
So, we have:
![\mathbf{A' = 2 \times (4,-2) = (8,-4)}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%27%20%3D%202%20%5Ctimes%20%284%2C-2%29%20%3D%20%288%2C-4%29%7D)
![\mathbf{B' = 2 \times (-2,-2) = (-4,-4)}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%27%20%3D%202%20%5Ctimes%20%28-2%2C-2%29%20%3D%20%28-4%2C-4%29%7D)
![\mathbf{C' = 2 \times (-2,2) = (-4,4)}](https://tex.z-dn.net/?f=%5Cmathbf%7BC%27%20%3D%202%20%5Ctimes%20%28-2%2C2%29%20%3D%20%28-4%2C4%29%7D)
See attachment for the graph of A'B'C'
<u>(b) Dilate by scale factor 2 with center (0,0)</u>
We simply multiply the coordinates of ABC by 1/2
So, we have:
![\mathbf{A" = \frac 12 \times (4,-2) = (2,-1)}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%22%20%3D%20%5Cfrac%2012%20%5Ctimes%20%284%2C-2%29%20%3D%20%282%2C-1%29%7D)
![\mathbf{B" = \frac 12 \times (-2,-2) = (-1,-1)}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%22%20%3D%20%5Cfrac%2012%20%5Ctimes%20%28-2%2C-2%29%20%3D%20%28-1%2C-1%29%7D)
![\mathbf{C' = \frac 12 \times (-2,2) = (-1,1)}](https://tex.z-dn.net/?f=%5Cmathbf%7BC%27%20%3D%20%5Cfrac%2012%20%5Ctimes%20%28-2%2C2%29%20%3D%20%28-1%2C1%29%7D)
See attachment for the graph of A"B"C'
<u>(c) Is A"B"C" a dilation of A'B'C</u>
Yes, A"B"C" is a dilation of A'B'C
- <em>ABC is dilated by 2 to get A'B'C</em>
- <em>ABC is dilated by 1/2 to get A"B"C</em>
So, the scale factor (k) from A'B'C' to A"B"C" is:
![\mathbf{k = \frac{1/2}{2}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bk%20%3D%20%5Cfrac%7B1%2F2%7D%7B2%7D%7D)
![\mathbf{k = \frac 14}](https://tex.z-dn.net/?f=%5Cmathbf%7Bk%20%3D%20%5Cfrac%2014%7D)
The scale factor (k) from A'B'C' to A"B"C" is 1/4
And the center is (0,0)
Read more about dilations at:
brainly.com/question/13176891
Answer:
Each part is 3.5 inches long.
Step-by-step explanation:
The ruler has a length of 7-inches, so when you want to split it directly in half, you divide 7/2. This is the number 3.5 inches. On the ruler you can see when looking at the first segment that it goes from 0 inches to half-way between 3 inches and 4 inches, which is 3.5 inches.
Answer: 0.614
Step-by-step explanation:
First find the probability that he catches the bus in a day.
Probability of catching bus once = 1 - Probability of missing bus
= 1 - 0.15
= 0.85
If he arrives on 3 consecutive days at 7:30 am, the probability he will catch the bus is:
= (P | Day 1) * (P | Day 2) * (P | Day 3)
= 0.85 * 0.85 * 0.85
= 0.614
Answer:
$4687.50/minute
Step-by-step explanation:
First find how much the athlete earned each day.
Divide total earnings by number of games.
$18,000,000 ÷ 80 games = $225,000/game
Find out the earnings per minute.
Divide that number by the number of minutes in each game.
$225,000 ÷ 48 minutes = $4687.50/minute
Therefore the athlete earned $4687.50 per minute.