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The 3D graphic below shows a garage door - Leaving Cert DCG - Question A-1 - 2012
Question A-1
The 3D graphic below shows a garage door. The top of the door is in the shape of a semi-ellipse. In the drawing of the door on the right, AB is the major axis of the... show full transcript
Worked Solution & Example Answer:The 3D graphic below shows a garage door - Leaving Cert DCG - Question A-1 - 2012
Step 1
Locate the minor axis of the ellipse.
Answer
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Locate midpoint of AB: To find the midpoint, use the formula for the midpoint between two points A and B, given as:
In this case, find the coordinates of points A and B in the diagram, and calculate the midpoint M.
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Draw minor axis line: From the midpoint M, draw a vertical line segment perpendicular to the major axis AB. This line represents the minor axis of the ellipse.
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Locate end points of minor axis: To locate the endpoints of the minor axis, measure the distance from M to the ellipse and mark the points above and below M. These points define the vertical span of the ellipse.
Step 2
Draw the semi-ellipse.
Answer
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Appropriate method of construction: Use the traditional ellipse construction method, such as the string and pins technique, where two focal points (F1, F2) are fixed.
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Locate points on curve: By varying the length of the string and moving it around the fixed foci, trace out points that form the upper half of the ellipse, ensuring that all points satisfy the ellipse equation:
where P represents any point on the ellipse and a is the semi-major axis length.
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Draw curve: Connect all the points smoothly to form the upper curve of the ellipse, which is the required semi-ellipse for the garage door.
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Presentation: Ensure that the drawing is neat, all lines are clear, and points are accurately marked for clarity and professionalism.