Photo AI
Glamping or glamorous camping appeals to those seeking adventure while on holiday - Leaving Cert DCG - Question A-2 - 2017
Question A-2
Glamping or glamorous camping appeals to those seeking adventure while on holiday. In the given drawing a portion of one parabola is inscribed in the rectangle VABC.... show full transcript
Worked Solution & Example Answer:Glamping or glamorous camping appeals to those seeking adventure while on holiday - Leaving Cert DCG - Question A-2 - 2017
Step 1
Locate the remaining points on the semi-parabola in the rectangle VABC and complete this curve.
Answer
To locate the remaining points on the semi-parabola, we first identify the vertex V located on the vertical axis of symmetry of the parabola. The equation of a standard parabola open upwards is given by: where (h, k) is the vertex. Given that the vertex V is at a point (h, k), we can determine the 'a' value by considering the distance from V to points A and C.
-
Determine the Axis of Symmetry: The line BC acts as the axis of symmetry. The x-coordinate of vertex V represents the midpoint between points A and C.
-
Calculate Points A and C: To complete the parabola, find points A and C such that they are equal distances from V along the x-axis while maintaining the parabolic curve. We plot the reflected points symmetrically from the vertex V.
-
Complete the Curve: Connect the points to form the upper semi-parabolic curve within the rectangle VABC.
Step 2
The second semi-parabola, in rectangle VDBC, is a mirror image of the first parabola, with BC as the axis of symmetry.
Answer
To draw the second semi-parabola:
-
Identify the Mirror Image Properties: Since BC is the axis of symmetry, points on the first semi-parabola will have mirrored counterparts across line BC.
-
Determine the Equation of the Original Parabola: Let us denote the original parabola as , as previously determined. The second parabola can be derived from this by reflecting across line BC.
-
Mirror Points: For every point (x, y) on the original parabola, the mirrored point will be (x, -y + 2k) where k is the same vertical position of line BC (midpoint along the vertical axis).
-
Plot the Mirror Points: Using the points derived from the original parabola, plot the new points for the second parabola using the transformations determined.
-
Draw the Completed Second Semi-Parabola: Connect these points smoothly to form a downward-facing semi-parabola that is a mirror image of the first.