Question

Absolute coordinates are coordinate values measured relative to the origin point (the 0,0,0) point. a) true b) false

Answer 1

The statement "Absolute coordinates are coordinate values measured relative to the origin point (the 0,0,0) point" is true. A vector can indeed form a right-angle triangle with its components, allowing the use of the Pythagorean theorem to calculate its magnitude. Option A.

Step-by-step explanation:

Absolute coordinates are measured relative to the origin point (0,0,0), and this statement is true. In a Cartesian coordinate system, the origin is where the x, y, and z-axes intersect, and absolute coordinates are given relative to this point. Therefore, the answer to the question is (a) true.

A vector can form the shape of a right-angle triangle with its x and y components, which is also true. This concept is particularly useful when you need to ascertain the magnitude and direction of the resultant vector using trigonometric methods, such as the Pythagorean theorem and inverse tangent functions to find the components and angle respectively.

For example, considering a coordinate system in which the positive x-axis is directed upward vertically, a particle located 5.0 m directly above the origin would be at coordinates (0, 5.0) in a 2D system or (0, 5.0, 0) in a 3D system. Similarly, a particle 2.0 m below the origin would be at (0, -2.0) or (0, -2.0, 0), respectively.

Lastly, it is true that we can use the Pythagorean theorem to calculate the length of the resultant vector from the addition of two orthogonal vectors, as these two vectors would form the perpendicular sides of a right triangle with the resultant being the hypotenuse.

Hence, the statement is true. Option A.

Answer 2

Absolute coordinates in a geometric or CAD context are indeed coordinate values measured relative to the origin point (the 0,0,0 point). Therefore, the correct answer is option a) True.

Step-by-step explanation:

In geometric and Computer-Aided Design (CAD) systems, absolute coordinates refer to positions measured relative to a fixed origin point, often denoted as the 0,0,0 point. This origin serves as the reference point for establishing the x, y, and z coordinates of other points in the space.

For instance, if a point P has absolute coordinates (x, y, z), it means the distance along the x-axis, y-axis, and z-axis from the origin to point P is precisely defined. These absolute coordinates are essential for accurately locating and describing geometric entities, such as points, lines, or objects, within a given coordinate system.

In a three-dimensional space, the concept of absolute coordinates becomes crucial for precise positioning. The origin point (0,0,0) serves as the starting reference, and absolute coordinates provide a systematic way to express the location of any point in the space.

This mathematical representation ensures consistency and precision in geometric calculations and design tasks. Whether in architectural design, engineering, or any field utilizing CAD systems, understanding and working with absolute coordinates is fundamental for accurate and standardized representation of spatial relationships.

In conclusion, the statement is true as absolute coordinates are, by definition, measured relative to the origin point, providing a standardized and systematic approach to specifying the positions of points in geometric or CAD environments.