Video Transcript
The quadrilateral π΄π΅πΆπ· in the
given figure has been dilated from the center point π₯ to the quadrilateral π΄ dash
π΅ dash πΆ dash π· dash. What is the scale factor of the
dilation?
So, in this question, weβre given a
four-sided shape, π΄π΅πΆπ·. The image of π΄π΅πΆπ· is this
smaller quadrilateral shown. And weβre told itβs dilated from
the center point π₯. Now, normally, to find the scale
factor of the dilation, we can use a formula. We find two corresponding sides,
one on each of our shapes. The scale factor is the length of
the side on the image divided by the length of the side on the original shape. And so, in this case, for example,
we could take the length of the side π΄π· and the length of the side π΄ dash π·
dash.
If we take one small square to be
one unit, then π΄ dash π· dash is 10 units in length. Similarly, the side length π΄π· is
20 units. So, we could say that the scale
factor of enlargement was 10 divided by 20, which is equal to one-half. In this case, though, thatβs not
the end of the story. If we join rays connecting π΄ and
π΄ dash and π· and π· dash, they pass through the center point π₯. And we should recall that an
enlargement using a negative scale factor achieves this. It causes the enlargement to appear
on the other side of the center, and itβs also inverted as our shapes are.
So, in this case, the scale factor
of enlargement or the scale factor of dilation is actually negative one-half.
