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The image below shows the Wembley arch that supports the roof of the football stadium - Leaving Cert DCG - Question A-2 - 2022
Question A-2
The image below shows the Wembley arch that supports the roof of the football stadium. The arch is in the shape of a parabola. The drawing on the right shows a porti... show full transcript
Worked Solution & Example Answer:The image below shows the Wembley arch that supports the roof of the football stadium - Leaving Cert DCG - Question A-2 - 2022
Step 1
Locate the remaining points on the left hand side of the parabola.
Answer
To find the points on the left-hand side, we first divide the line segment AB into equal sections based on the desired number of points. After determining the proportions, we can identify corresponding points along the parabolic curve by applying symmetry about the vertex V.
- Divide line AB into equal segments based on the total segments required.
- Locate the points by referencing the vertex V and applying quadratic functions to get the respective y-values.
Step 2
Locate the points on the right hand side of the parabola.
Answer
For the right-hand side, similar segmentation can be carried out as done on the left. After determining the intervals, we can map the parabolic curve points corresponding to those segments.
- Using the same intervals as the left side, calculate the y-coordinates for the points on line BC by applying the parabolic formula.
Step 3
Complete the parabola in the rectangle ABCD.
Answer
To complete the parabolic shape, connect the identified points on both the left and right sides smoothly to ensure continuity.
- Draw a smooth curve that transitions through the points identified on both the left and right-hand sides, ensuring the curve passes through the vertex V.
- Make sure that the curve approaches the sides of rectangle ABCD, retaining the parabolic shape as seen in the figure.