Final answer:
The equation d = sqrt(delta x^2 + delta y^2) calculates the magnitude of a resultant vector and is valid when the components x and y are perpendicular to each other, making an angle of 90 degrees. This is based on the Pythagorean theorem used in physics for vectors that lie within the xy-plane.
Step-by-step explanation:
The equation d = \( \sqrt{\Delta x^2 + \Delta y^2} \) is a representation of how to calculate the magnitude of a resultant vector d from its horizontal and vertical components, \( \Delta x \) and \( \Delta y \), in a two-dimensional space. This equation is derived from the Pythagorean theorem and is valid only if the vectors x and y are perpendicular to each other, i.e., they have an orientation of 90 degrees with respect to each other. When vectors are perpendicular, their components lie along the axes of a Cartesian coordinate system, such as the horizontal x-axis and the vertical y-axis.
To apply this formula, first resolve the vector into its perpendicular components along the x and y axes. When you know these components, you can then use the equation to find the magnitude of the resultant vector. Thus, this equation is frequently used in physics to determine the displacement of an object when it moves along two perpendicular directions within the xy-plane.