Question

Where will the image of O be located after a dilation by a scale factor of (1/3) centered at the origin?

a) At the origin
b) On a line parallel to the y-axis
c) On a line parallel to the x-axis
d) On a line with a slope of 3

Answer 1

After a dilation centered at the origin with a scale factor of (1/3), the image of the point O, which is located at the origin, will remain at the origin.

Step-by-step explanation:

The location of the image of O after a dilation by a scale factor of (1/3) centered at the origin can be determined by applying the properties of dilations in a coordinate system. Since O is at the origin (0,0) and the scale factor is (1/3), we multiply the coordinates of O by 1/3. However, since O is at the origin, multiplying by any scale factor will still result in the coordinates (0,0). Therefore, the image of O after the dilation will remain at the origin.