Fig. B-2 shows an incomplete trimetric projection, using the axonometric axes method, of a model of a basketball backboard, based on the 3D graphic on the right - Leaving Cert DCG - Question B-2 - 2014

To draw the scalene triangle abc:

1. Use the coordinates provided in the figure to plot the points a, b, and c in the axonometric view.
2. Connect the points using straight lines to form a triangle. Ensure that the triangle does not have any equal sides or angles, confirming its scalene nature.

To draw the X-axis:

1. Extend a horizontal line from the origin point where the Y and Z axes meet.
2. Label this line as the X-axis, ensuring it is parallel to the ground in the axonometric view.

For the elevation and end view:

1. Ensure the XY plane is properly oriented by projecting the corresponding points of the axonometric drawing.
2. The development of the YZ plane is established based on the elevation drawing provided, ensuring the correct angles and dimensions are represented.
3. Ensure that the top view is correctly drawn in elevation based on the orientation of X and Y plane.

To draw the axonometric projection of the basketball:

1. Start from point P where the basketball makes contact with the backboard.
2. Represent the basketball as a circle in the axonometric view, ensuring the radius of 12mm is correctly applied.
3. Draw the basketball in a manner that reflects the curvature interacting with the backboard.

To determine points on the curve:

1. Identify at least 5 key points along the curve of the basketball's surface in relation to the backboard.
2. Use precise measurements from the center to ensure each point corresponds accurately in the axonometric view.

To draw the curve:

1. Connect the points designated along the basketball's edge smoothly to represent its curvature.
2. Ensure the curve reflects the spherical nature of the basketball while maintaining a focus on the tangential properties with the backboard.

To locate the center of the sphere:

1. From the projection, find the center of the basketball by measuring 12mm from point P.
2. Ensure the center lies accurately in the axonometric corner where the X, Y, and Z axes intersect.

To draw the radius of the sphere:

1. Mark a circular area around the center that corresponds to the radius of 12mm.
2. Ensure the radius is drawn in a way that complements the existing axonometric projection of the basketball.