Question

Polygon ABCDE is dilated about the origin to create polygon ABCDEWhat is the scale factor of the dilation if point E (5, 3) becomes E (15, 9) ?

Answer 1

To find the dilation scale factor, divide the new coordinates by the original coordinates. In this case, the scale factor is 3 because point E's coordinates (5, 3) have been multiplied by 3 to become (15, 9).

Step-by-step explanation:

The student asked about the scale factor of a dilation given that point E (5, 3) becomes E' (15, 9). To find the scale factor, we compare the coordinates of E and E' to determine how much E has been stretched to become E'.

By comparing the x-coordinates (5 and 15), we can see that 15 is three times 5. Similarly, by comparing the y-coordinates (3 and 9), we can see that 9 is three times 3. This indicates that the dilation scale factor is 3, because both the x and y coordinates of point E have been multiplied by 3 to get the coordinates of E'.

Step-by-step explanation:

1. Take the coordinates of point E before the dilation, which are (5, 3).
2. Take the coordinates of point E after the dilation, which are (15, 9).
3. Divide the new coordinates by the original coordinates separately: 15/5 = 3 and 9/3 = 3.
4. Since both the x and y coordinates are multiplied by the same number, that number is the dilation scale factor.