Question

The coordinate notation shows how the coordinate of a figure are related to the coordinates of its image after transformations. What are the transformations? Are the figure and its image congruent? Explain.

$(\mathrm{x},\mathrm{y})\to (2\mathrm{x}+4,2\mathrm{y}-3)$

Answer 1

Check the transformations of coordinates.

Given, coordinates are $(\mathrm{x},\mathrm{y})\to (2\mathrm{x}+4,2\mathrm{y}-3)$

From coordinates we can observe,

1. Here, both $\mathrm{x}-$coordinate and $\mathrm{y}-$coordinate has been doubled which means that the point has been dilated by the scale factor of $2$.
2. And, we can see that $4$ has been added $\mathrm{x}-$coordinate while $3$ is added to $\mathrm{y}-$coordinate which means that the coordinates obtained after the dilation has been translated $4$ unit right (because positive) and $3$ units down (because negative)

Hence, the final image will not be congruent because after dilation the size of the image either increases or decreases, due to which original figure and are not congruent.