Point M(2, 4) was dilated to M’(9, 18). What was the scale factor
the scale factor was 9/2 or 4.5
To find the scale factor of the dilation, we need to determine the ratio of the corresponding side lengths between the original point and the dilated point.
The distance between the x-coordinates of the original point and the dilated point is (9 - 2) = 7.
The distance between the y-coordinates of the original point and the dilated point is (18 - 4) = 14.
So, the scale factor is given by the ratio of these distances:
Scale factor = (distance between dilated x-coordinates) / (distance between original x-coordinates)
= 7 / (9 - 2)
= 7 / 7
= 1
Similarly,
Scale factor = (distance between dilated y-coordinates) / (distance between original y-coordinates)
= 14 / (18 - 4)
= 14 / 14
= 1
Since the ratio is the same for both x and y coordinates, the scale factor for this dilation is 1.
To find the scale factor in a dilation, we need to compare the corresponding side lengths or distances of the original point with the corresponding side lengths or distances of the dilated point.
In this case, we have the original point M(2, 4) and the dilated point M’(9, 18).
The distance between the x-coordinates of the two points is (9 - 2) = 7, and the distance between the y-coordinates of the two points is (18 - 4) = 14.
To calculate the scale factor, we divide the change in the x-coordinate of the dilated point by the change in the x-coordinate of the original point, and also divide the change in the y-coordinate of the dilated point by the change in the y-coordinate of the original point.
So, the scale factor in this case would be:
Change in x-coordinate: 7 / (2 - 2) = 7 / 0 (undefined)
Change in y-coordinate: 14 / (4 - 4) = 14 / 0 (undefined)
However, the scale factor in this case is undefined because both the x-coordinate and y-coordinate did not change.
This means that the original point and the dilated point are the same, and there was no scaling involved.