Apply a Stipulated Projection Relationship

Supplied materials

• Paper and a pencil, typed notes or a browser scratch area. Color names can replace colored supplies; drawn figures and timelines can replace performance.
• Complete teaching inputs: For a supplied perspective model, projected width is constantK divided by distance. At distance2, width is24 units. What width does the same model give at distance4? Supplied candidates: (A) 11 units (B) 12 units (C) 13 units (D) 14 units.
• Independent check: For a supplied perspective model, projected width is constantK divided by distance. At distance3, width is24 units. What width does the same model give at distance9? Supplied candidates: (A) 10 units (B) 7 units (C) 8 units (D) 9 units.

Learn the idea

Link a design’s purpose, representation and evidence. Prioritize required information, apply a stipulated projection model, construct an argument from visible features and organize a portfolio so a reviewer can trace revision decisions. Under the supplied model, projected width equals a constant divided by distance. Derive the constant from one complete observation, then use the new distance instead of assuming width changes additively.

Reason through the supplied case: The first observation gives K=24×2=48. The farther width is K/4=12. This inverse-distance projection is a stipulated simplified model, not a measured rule for every artwork or real-world camera.

This inverse-distance relationship is a simplified exercise model. It does not establish every camera’s behavior or the physical scale of an artwork from a description.

1. Read the complete teaching inputs and mark the feature, rule or constraint being tested.
2. Compare the model decision with one rejected candidate; state the visible evidence or calculation that distinguishes them.
3. Solve the independent check and the three changed-input practice cases before reading feedback.
4. Use width twenty-four at distance three to predict width at distance nine, showing the inferred constant.
5. Check your artifact against these explicit criteria: The constant is seventy-two and the predicted width is eight units under the supplied model.

Check your reasoning

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Take it further

New-input analysis: For a supplied perspective model, projected width is constantK divided by distance. At distance5, width is24 units. What width does the same model give at distance15? Supplied candidates: (A) 10 units (B) 7 units (C) 8 units (D) 9 units. Expected relationship: 8 units. The first observation gives K=24×5=120. The farther width is K/15=8. This inverse-distance projection is a stipulated simplified model, not a measured rule for every artwork or real-world camera. Create your own artifact: Use width twenty-four at distance three to predict width at distance nine, showing the inferred constant. Completion criteria: The constant is seventy-two and the predicted width is eight units under the supplied model.

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