Question

Veronica performs a dilation on figure A. She uses a scale factor of 3 with a center of dilation at the origin. She says the coordinates of the image of point X are (3, 12). What mistake may Veronica have made, and what are the correct coordinates of the image? Explain your reasoning.

Answer 1

Veronica may have mistaken the calculation of coordinates after a dilation by incorrectly applying the scale factor, but the correctness of Veronica's coordinates depends on the original position of point X which is not provided.

Step-by-step explanation:

The mistake Veronica may have made is in calculating the coordinates of the image of point X after performing a dilation with a scale factor of 3. If we assume the original coordinates of point X are (x,y), then after the dilation, the new coordinates would be (3x, 3y) since each coordinate is multiplied by the scale factor. Therefore, if Veronica says the new coordinates are (3, 12), this suggests the original coordinates of point X were (1, 4). To determine the correct coordinates of the image, we would need the original coordinates of X. Without this information, we can only say that Veronica's statement might imply a mistake if point X’s original coordinates were not (1, 4). If the original coordinates were indeed (1, 4), then there is no mistake, and (3, 12) would in fact be the correct image coordinates after the dilation.