Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.
DIlations are defined by the follwing operation:
[tex]P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)][/tex] (1)
Where:
If we know that [tex]O(x,y) = (1,1)[/tex], [tex]k = 0.5[/tex], [tex]J(x,y) = (3,1)[/tex], [tex]K(x,y) = (5, -3)[/tex], [tex]L(x,y) = (5,5)[/tex] and [tex]M(x,y) = (3,7)[/tex], then the coordinates of the new polygon are:
[tex]J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)][/tex]
[tex]J'(x,y) = (1,1)+0.5\cdot (2,0)[/tex]
[tex]J'(x,y) = (1,1) +(1,0)[/tex]
[tex]J'(x,y) = (2,1)[/tex]
[tex]K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)][/tex]
[tex]K'(x,y) = (1,1) +0.5\cdot (4,-4)[/tex]
[tex]K'(x,y) = (1,1) +(2,-2)[/tex]
[tex]K'(x,y) = (3,-1)[/tex]
[tex]L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)][/tex]
[tex]L'(x,y) = (1,1) + 0.5\cdot (4,4)[/tex]
[tex]L'(x,y) = (1,1) + (2,2)[/tex]
[tex]L'(x,y) = (3,3)[/tex]
[tex]M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)][/tex]
[tex]M'(x,y) = (1,1) +0.5\cdot (2,6)[/tex]
[tex]M'(x,y) = (1,1) +(1,3)[/tex]
[tex]M'(x,y) = (2,4)[/tex]
Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.
We kindly invite to check this question on dilations: https://brainly.com/question/13176891
