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HELP ME PLEASE 100 POINTS
1. Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:

Octagon ABCDEFGH with ordered pairs at A at 2, 1, at B 2, negative 1, C 1, negative 2, D negative 1, negative 2, E negative 2, negative 1, F negative 2, 1, G negative 1, 2, H 1, 2. Octagon A prime B prime C prime D prime E prime F prime G prime H prime with ordered pairs A prime 8, 4, at B prime 8, negative 4, at C prime 4, negative 8, at D prime negative 4, negative 8, at E prime negative 8, negative 4, at F prime negative 8, 4, at G prime negative 4, 8, at H prime 4, 8.

If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated?

one half
one quarter
2
4

2.A toy company manufactures arcade games. They are marketing a new pinball machine to children. It is similar in size to the adult version of the same game. Both the adult and child models are shown below:

Adult pinball machine GAME with base ME measuring 35 inches and sides measuring 56 inches. Child pinball machine G prime A prime M prime E prime with base M prime E prime measuring 14 inches

If the perimeter of the adult pinball machine is 177 inches, what is the length, in inches of Segment line G prime A prime? Type the numeric answer only in the box below.

Numerical Answers Expected!

Answer for Blank 1:

3.Hexagon IJKLMN is shown on the coordinate plane below:

Hexagon IJKLMN on a coordinate plane with ordered pairs at I negative two, six, at J four, four, at K six, negative one at, L negative one, two, at M negative four, negative four, at N negative six, two

If hexagon IJKLMN is dilated by a scale factor of two fifths from the origin to create hexagon I'J'K'L'M'N', what is the ordered pair of point I'?

(−0.8, 2.4)
(−5, 15)
(−2.5, 5)
(−0.4, 0.8)

4.Pentagon OPQRS is shown on the coordinate plane below:

Pentagon OPQRS on a coordinate plane with ordered pairs at O negative 1, 2, at P negative 5, 3, at Q negative 3, negative 2, and R 2, 1, at S 2, 5.

If pentagon OPQRS is dilated by a scale factor of seven over four from the origin, to create O'P'Q'R'S', what is the ordered pair of point S'?

(8.75, 5.25)
(1.25, 0.75)
(1.75, 3.5)
(3.5, 8.75)

5.Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three eighths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television?

7.5 inches by 15 inches
28 inches by 56 inches
32 inches by 64 inches
4.5 inches by 9 inches
i need to get caught up help is appreciated

Respuesta :

Answer:

#1) 4; #2) 12 inches; #3) (-0.8, 2.4); #4) (3.5, 8.75); #5) 32 inches by 64 inches

Explanation:

#1) To get the image points, each pre-image point was multiplied by 4.  This means that the scale factor is 4.

#2) The perimeter of GAME is 177.  We know that three of the sides are 35, 56 and 56.  This means the fourth side, GA, would be

177-(35+56+56) = 177-147 = 30 inches

This means that GA to G'A' would have the same ratio as ME to M'E'; this gives us the proportion

[tex]\frac{35}{14}=\frac{30}{x}[/tex]

Cross multiplying, we have

35(x) = 14(30)

35x = 420

Divide both sides by 35:

35x/35 = 420/35

x = 12

#3) To find the coordinates of I', we multiply the coordinates of I by the scale factor:

I' = (-2(2/5), 6(2/5)) = (-4/5, 12/5) = (-0.8, 2.4)

#4) To find the coordinates of S', multiply the coordinates of S by the scale factor:

S' = (2(7/4), 5(7/4)) = (14/4, 35/4) = (3.5, 8.75)

#5) The generic version is 3/8 the size of the brand name version.  This means that the brand name version is 8/3 of the generic version.  To find the dimensions of the brand name version, we multiply the dimensions of the generic version by 8/3:

12(8/3) = 96/3 = 32

24(8/3) = 192/3 = 64

The dimensions of the generic version are 32 by 64.

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