Let’s look at dilations in the coordinate plane.
Explore the applet and observe the dilation of triangle $ABC$. The dilation always uses center $P$, but you can change the scale factor. What connections can you make between the scale factor and the dilated triangle?
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
If your teacher gives you the data card:
Triangle $EFG$ was created by dilating triangle $ABC$ using a scale factor of 2 and center $D$. Triangle $HIJ$ was created by dilating triangle $ABC$ using a scale factor of $\frac12$ and center $D$.
What would the image of the triangle look like under dilation with a scale factor of -1? If possible, draw it and label the vertices $A’$, $B’$, and $C’$. If it’s not possible, explain why not.
If possible, describe what happens to a shape if it is dilated with a negative scale factor. If dilating with a negative scale factor is not possible, explain why not.
One important use of coordinates is to communicate geometric information precisely. Let’s consider a quadrilateral $ABCD$ in the coordinate plane. Performing a dilation of $ABCD$ requires three vital pieces of information:
With this information, we can dilate the vertices $A$, $B$, $C$, and $D$ and then draw the corresponding segments to find the dilation of $ABCD$. Without coordinates, describing the location of the new points would likely require sharing a picture of the polygon and the center of dilation.
