The discussion clarifies the scaling of a rectangle in the plane, specifically the rectangle defined by vertices (-1,0), (-1,1), (1,1), and (1,0). When scaled by a positive scalar λ, the resulting rectangle λD has vertices at (-λ, 0), (-λ, λ), (λ, λ), and (λ, 0). For example, scaling by 2 results in the rectangle with vertices (-2,0), (-2,2), (2,2), and (2,0). This confirms that scaling a geometric shape by a factor expands or contracts its dimensions proportionally.
PREREQUISITESMathematicians, geometry enthusiasts, students studying linear algebra, and anyone interested in geometric transformations and their properties.
Your interpretation seems reasonable to me, although I've never run into any other situations where a set was multiplied by a number.Mr Davis 97 said:This is a pretty simple question, I am just trying to clear up confusion. Let ##D## be the rectangle in the plane with vertices ##(-1,0),(-1,1),(1,1),(1,0)##. Let ##\lambda >0##. Then what exactly does the set ##\lambda D## look like? Is it correct to say that, for example, ##2D## is the rectangle with vertices ##(-2,0),(-2,2),(2,2),(2,0)##?
Mark44 said:Your interpretation seems reasonable to me, although I've never run into any other situations where a set was multiplied by a number.