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Rosa is looking at a map of the park that is laid out on a coordinate plane. Rosa is at(1, -1). The shelter house is at (-2, -4) and the fossil exhibit is at (3, 2). Each unit on the map represents 100 feet. How much closer is rosa to the fossil exhibit than to the shelter house

Respuesta :

SageRage

Answer:

[tex]63.709feet[/tex]

Step-by-step explanation:

  • This deals with the distance between two points
  • use the equation [tex]distance=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
  • So we do the follow steps
  1. Find distance from Rosa to Shelter house
  2. Find distance from Rosa to Fossil exhibit
  3. Subtract the two answers to see difference
  • So distance from Rosa to Shelter, we use (1,-1) and (-2,-4) so you plug your points in as follows [tex](1,-1)=(x_1,y_1)[/tex] and [tex](-2,-4)=(x_2,y_2)[/tex]  so then
  • [tex]distance=\sqrt{((-2)-(1))^{2}+((-4)-(-1))^{2}}\\ distance=\sqrt{(-3)^{2}+(-3)^{2}}\\ distance=\sqrt{9+9}\\ distance=\sqrt{18}=4.24264[/tex] approximately (round off as they require)
  • Now putting that into feet [tex]4.24264*100feet=424.264feet[/tex]
  • Then next, distance from Rosa to Fossil exhibit, we use (1,-1) and (3,2) so you plug your points in as follows
  • [tex]distance=\sqrt{((3)-(1))^{2}+((2)-(-1))^{2}}\\ distance=\sqrt{(2)^{2}+(3)^{2}}\\ distance=\sqrt{4+9}\\ distance=\sqrt{13}=3.60555[/tex]    approximately (round off as they require)
  • Now putting that into feet [tex]3.60555*100feet=360.555feet[/tex]
  • So right away we know, Rosa is closer to the Fossil exhibit than the Shelter
  • Then to know by how much we subtract the longer distance from the shorter so [tex]424.264feet-360.555feet=63.709feet[/tex]

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