## 4.1: Estimating a Scale Factor

Point $C$ is the dilation of point $B$ with center of dilation $A$ and scale factor $s$. Estimate $s$. Be prepared to explain your reasoning.

Let’s dilate figures on a rectangular grid.

- Find the dilation of quadrilateral $ABCD$ with center $P$ and scale factor 2.
- Find the dilation of triangle $QRS$ with center $T$ and scale factor 2.
- Find the dilation of triangle $QRS$ with center $T$ and scale factor $\frac{1}{2}$.

Your teacher will give you some cards. Each of Cards 1 through 6 shows a figure in the coordinate plane and describes a dilation.

Each of Cards A through E describes the image of the dilation for one of the numbered cards.

Match number cards with letter cards. One of the number cards will not have a match. For this card, you’ll need to draw an image.

Square grids can be useful for showing dilations. The grid is helpful especially when the center of dilation and the point(s) being dilated lie at grid points. Rather than using a ruler to measure the distance between the points, we can count grid units.

Sometimes the square grid comes with coordinates. The coordinate grid gives us a convenient way to *name* points, and sometimes the coordinates of the image can be found with just arithmetic.