Question

1. dilate point a, located at (9,7) from center o, by a scale - factor r = 4/9. then, dilate point b, located at center o, by a scale factor of r = 4/9. what are the coordinates of points a and b? explain.
2. explain how you used the fundamental theorem of similarity in problems 1 and 2.

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated from the origin $(0,0)$ by a scale - factor $r$, the new coordinates $(x',y')$ are given by $(x',y')=(r\times x,r\times y)$. Here, the center of dilation is the origin $O(0,0)$, the point $A$ has coordinates $(9,7)$ and the scale - factor $r = \frac{4}{9}$.

Step2: Calculate the $x$ - coordinate of $A'$

$x'=r\times x=\frac{4}{9}\times9 = 4$.

Step3: Calculate the $y$ - coordinate of $A'$

$y'=r\times y=\frac{4}{9}\times7=\frac{28}{9}$.

Answer:

The coordinates of point $A'$ are $(4,\frac{28}{9})$.