Question

The transform of M:

(x,y) -> (0.3x,0.3y) has been applied to the polygon KLM. if the point M had coordinates (6,6) name the coordinates of image M.

Answer 1

The coordinates of the image point M, after applying a scaling transformation with a factor of 0.3 to the original point (6, 6), are (1.8, 1.8).

The transformation applied to the polygon KLM is a scaling transformation, which rescales the coordinates of each point by a factor of 0.3 along both the x and y axes. For the point M with original coordinates (6, 6), the transformation yields new coordinates by multiplying each original coordinate by 0.3.

Mathematically, the transformation can be expressed as follows:

`\[ \text{New } M = (0.3 * 6, 0.3 * 6) = (1.8, 1.8) \]`

This means that the x-coordinate of M is transformed to 1.8, and the y-coordinate is also transformed to 1.8.

In geometric terms, the effect of the transformation is a contraction or shrinking of the original polygon. The image of M is positioned at (1.8, 1.8) in the transformed polygon K' L' M', where each point's coordinates are rescaled by a factor of 0.3.

Understanding transformations, such as scaling, is crucial in geometry and computer graphics, as they provide a way to manipulate and visualize the changes in shapes and figures. The coordinates (1.8, 1.8) represent the new location of point M after the scaling transformation has been applied.