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Explain the term "perspective"

Mathematics

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Answer

5 metres

Step-by-step solution

6 steps
  1. Question 1 - Scale for length

    1 cm on the map represents 100 cm in real life.

    1 cm(map)=100 cm(real)=1 m1\ \mathrm{cm(map)} = 100\ \mathrm{cm(real)} = 1\ \mathrm{m}

    Tick the first option.

  2. Question 1 - Scale for area

    Linear scale factor = 100.
    Area scale factor = 1002=10 000100^{2} = 10\,000.

    1 cm2(map)=10 000 cm2(real)=1 m21\ \mathrm{cm}^{2}(\mathrm{map}) = 10\,000\ \mathrm{cm}^{2}(\mathrm{real}) = 1\ \mathrm{m}^{2}

    The second option (100 square cm = 1 square metre) is incorrect.
    Do not tick the second option.

  3. Question 2 - Fill in the blanks

    It is 100 metres smaller when looking at a view or a photograph of it.
    Your eye makes distant objects appear smaller because closer to you appear bigger.
    This is called perspective.

  4. Explain the term “perspective”

    Perspective is the visual effect where distant objects appear smaller than closer objects of the same actual size.

  5. Question 3 - Why maps are more accurate

    Sketch maps are drawn as plan views (looking straight down from above). All distances are to scale with no distortion.
    Perspective drawings (side views) make distant objects look smaller, so distances between objects are not accurate.

  6. Question 4 - Distance from home to school using the sketch map

    The sketch map uses scale 1 cm(map)=1 m(real)1\ \mathrm{cm(map)} = 1\ \mathrm{m(real)}.
    Measure the path from home to school on the map (total length along the route).
    Assume map distance = 5 cm (from image: home to corner 2 cm + corner to school 3 cm).
    Real distance = map distance ×\times scale factor.

    5 cm(map)×100 cm(real)1 cm(map)=500 cm(real)=5 m5\ \mathrm{cm(map)} \times 100\ \frac{\mathrm{cm(real)}}{1\ \mathrm{cm(map)}} = 500\ \mathrm{cm(real)} = 5\ \mathrm{m}

    5 metres

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