Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The <em>original</em> polygon is highlighted in <em>red</em> and the image is highlighted in <em>blue</em>.
DIlations are defined by the follwing operation:
(1)
Where:
- Center of dilation.
- Dilation factor.
- Original point of the polygon.
- Dilated point of the polygon.
If we know that
,
,
,
,
and
, then the coordinates of the new polygon are:
![J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)]](https://tex.z-dn.net/?f=J%27%28x%2Cy%29%20%3D%20%281%2C1%29%20%2B%200.5%5Ccdot%20%5B%283%2C1%29-%281%2C1%29%5D)



![K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)]](https://tex.z-dn.net/?f=K%27%28x%2Cy%29%20%3D%20%281%2C1%29%20%2B%200.5%5Ccdot%20%5B%285%2C-3%29-%281%2C1%29%5D)



![L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)]](https://tex.z-dn.net/?f=L%27%28x%2Cy%29%20%3D%20%281%2C1%29%20%2B%200.5%5Ccdot%20%5B%285%2C5%29-%281%2C1%29%5D)



![M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)]](https://tex.z-dn.net/?f=M%27%28x%2Cy%29%20%3D%20%281%2C1%29%20%2B%200.5%5Ccdot%20%5B%283%2C7%29-%281%2C1%29%5D)



Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The <em>original</em> polygon is highlighted in <em>red</em> and the image is highlighted in <em>blue</em>.
We kindly invite to check this question on dilations: brainly.com/question/13176891
Answer:
We have;
7 pencil boxes and 5 eraser boxes
Step-by-step explanation:
To find the smallest number of boxes that can be bought, what we simply do is to find the lowest common multiple of the content of each of the boxes
hence, we are going to find the lowest common multiple of 10 and 14
The lowest common multiple of 10 and 14 is 70
So the smallest number of pencil boxes that can be bought is 70/10 = 7
The smallest number of eraser boxes would be 70/14 = 5
Answer:
(-4/3), 0.4, 0.8, √2, √11
Step-by-step explanation:
√11=3.316624790355399849114932736670686683927088545589353597058
0.4
(-4/3) = -1.33333333333333333333333333333333333333333333333333333333
0.8
√2=1.414213562373095048801688724209698078569671875376948073176
Thus :
(-4/3)
0.4
0.8
√2
√11