Final answer:
The question has some typos, but it raises concepts about perpendicular bisectors in geometry and vector components in physics. It is true that a vector forms right-angle triangles with its components and the Pythagorean theorem can be used to find the resultant magnitude. However, for the GRASP CHECK, knowing only the angles of vectors is not enough to find the resultant angle of their addition.
Step-by-step explanation:
The statement provided seems to have some typos or confusion in its terms. However, understanding the underlying concepts of geometry and vector addition, we can address the core ideas associated with the question.
Perpendicular Bisector
The assumption that a perpendicular bisector of a segment in geometry simply means that the line cuts the segment into two equal lengths and forms a right angle with the segment. This fact alone, however, is not enough to prove that angle YXZ is congruent to angle YAZ without additional information, perhaps suggesting the student intended to reference triangles or additional congruences.
Vector Addition and Components
A vector can indeed form the shape of a right-angle triangle with its x and y components, as it reflects the triangle's hypotenuse with its adjacent and opposite sides being the x and y components, respectively. This is True, and the length of the resultant vector can be calculated using the Pythagorean theorem if the vectors are at right angles to each other, which is also True.
Furthermore, the given expressions Ax = A sin θ and Ay = A cos θ (assuming the '0' is a typographical error for θ, the Greek letter theta) are correct for calculating the x and y components of a vector where A is the magnitude of the vector and θ is the angle it makes with the x-axis. Therefore, every 2-D vector can indeed be represented by its x and y components, indicated by the horizontal and vertical lengths in a coordinate plane.
Vector Resultant Angle
If only the angles of two vectors are known, without the magnitudes, it is not possible to find the angle of the resultant vector. Therefore, the GRASP CHECK statement is False.
In summary, the assumption that a perpendicular bisector of is not sufficient on its own to establish congruence between angles or other geometric properties without additional context or information, and understanding vector components and the use of the Pythagorean theorem is essential in calculating vector magnitudes and directions.