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The image below shows a fragrance bottle and diffuser reeds - Leaving Cert DCG - Question A-4 - 2020
Question A-4
The image below shows a fragrance bottle and diffuser reeds. The given elevation and plan show two similar reeds represented by the skew lines AB and CD. (a) Determ... show full transcript
Worked Solution & Example Answer:The image below shows a fragrance bottle and diffuser reeds - Leaving Cert DCG - Question A-4 - 2020
Step 1
Determine the projections of the shortest horizontal line between the skew lines.
Answer
To find the shortest horizontal line between skew lines AB and CD, follow these steps:
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Draw line from A parallel to CD: Begin by drawing a line from point A that is parallel to line CD. This line will meet CD at some point, let's call it C'.
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Draw line from C parallel to AB: Similarly, draw a line from point C that is parallel to line AB. This line will intersect AB at a point which we will call B'.
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Determine plane of horizontal line: Identify the horizontal plane that contains both lines AB and CD. This is crucial as it helps visualize the points and their relationships in 3D space.
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Identify X1Y1 perpendicular to horizontal line: Construct a line named X1Y1, which is perpendicular to the horizontal line connecting points B' and C'. This forms a right-angled triangle that allows for further calculations.
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Projections of AB and CD on X1Y1: Project both lines AB and CD onto X1Y1 to visualize the shortest distance.
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X1Y2 perpendicular to X1Y1: Next, draw another perpendicular line named X1Y2 from X1Y1. This helps chart out the distance measurement more accurately.
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Projections of AB and CD on X1Y2: Project lines AB and CD onto X1Y2 to ascertain their distances in this plane.
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Projections of required shortest horizontal distance to plan and elevation: Finally, project the identified shortest horizontal distance to both the plan and elevation views. This gives a clear indication of the distance between AB and CD.
Step 2
Determine the true length of line AC.
Answer
To determine the true length of the line joining points A and C, we will utilize the following method:
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Draw line AC: Start by drawing the line directly connecting points A and C in the correct orientation.
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Constructing true length of line AC: Use the methods of projection identified previously. Measure the angles and the distances used to represent the line effectively.
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Use of construction methods: By employing methods such as triangulation or utilizing coordinate geometry, find the exact length of line AC. Use the Pythagorean theorem if necessary: ext{Length of AC} = rac{1}{2} imes ext{Base} imes ext{Height} or simply calculate by using the coordinates of points A and C if applicable.
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Conclusion: Present the calculated length of AC, ensuring all figures and drawings used are clearly annotated for reference.