Answer:
D'G' = 52.5 units
Step-by-step explanation:
Since the dilatation is centred at the origin then multiply the original coordinates by the scale factor 3.5
D' = (1 × 3.5, 7 × 3.5 ) = (3.5, 24.5 )
G' = (- 8 × 3.5, - 5 × 3.5 ) = (- 28, - 17.5 )
Calculate D'G' using the distance formula
d = ![\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%20%20%20%20%7D)
with (x₁, y₁ ) = D' (3.5, 24.5) and (x₂, y₂ ) = G' (- 28, - 17.5)
D'G' = ![\sqrt{(-28-3.5)^2+(-17.5-24.5)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-28-3.5%29%5E2%2B%28-17.5-24.5%29%5E2%7D)
= ![\sqrt{(-31.5)^2+42^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-31.5%29%5E2%2B42%5E2%7D)
= ![\sqrt{992.25+1764}](https://tex.z-dn.net/?f=%5Csqrt%7B992.25%2B1764%7D)
= ![\sqrt{2756.25}](https://tex.z-dn.net/?f=%5Csqrt%7B2756.25%7D)
= 52.5 units
Answer:
15
Step-by-step explanation:
15 gallons is the best because you get 15 gallons for 48.75 and 2gallons for free
exp. 20gal for $70
50quarts= 12.5 gal for $33.50
15 plus 2 gal is 17 for 48.75 much cheaper
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