The vertices of are F(2,1), G(4,1), and H(4,-1). The vertices of the image of the triangle after a dilation centered at (0,0) are F'(4,2), G'(8,2), and H'(8,-2). What is the scale factor of the dilation?

The scale factor of the dilation is 2

Step-by-step explanation:

The given vertices the ΔFGH are;

F(2, 1), G(4, 1), and H(4, -1)

The lengths of the sides of the triangle ΔFGH are;

The length of segment FG = √((4 - 2)² + (1 - 1)²) = 2

The length of segment FH = √((4 - 2)² + ((-1) - 1)²) = 2·√2

The length of segment GH = √((4 - 4)² + ((-1) - 1)²) = 2

After a dilation with the center of dilation = (0, 0), to give the ΔF'G'H', we have;

The given vertices the ΔF'G'H' are F'(4, 2), G'(8, 2), H'(8, -2)

The length of segment F'G' = √((8 - 4)² + (2 - 2)²) = 4

The length of segment F'H' = √((8 - 4)² + ((-2) - 2)²) = 4·√2

The length of segment G'H' = √((8 - 8)² + ((-2) - 2)²) = 4

The length of the sides of ΔFGH = 1/2 × The length of the sides of ΔF'G'H' or the length of the sides of ΔF'G'H' = 2 × The length of the sides of ΔFGH

Therefore, the scale factor of the dilation is 2.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.