To find the rule applied to the original rectangle to create the new rectangle, we can examine the original vertices and the corresponding dilated vertices to determine the relationship.
Original vertices:
- (12, 9)
- (12, -9)
- (-12, -9)
- (-12, 9)
Dilated vertices:
- (8, 6)
- (8, -6)
- (-8, -6)
- (-8, 6)
Now let's analyze the transformation for one of the points, for example, (12, 9) to (8, 6):
For the x-coordinate:
- From 12 to 8: \( 8 = k \cdot 12 \)
- \( k = \frac{8}{12} = \frac{2}{3} \)
For the y-coordinate:
- From 9 to 6: \( 6 = k \cdot 9 \)
- \( k = \frac{6}{9} = \frac{2}{3} \)
We see that both x and y coordinates are multiplied by \(\frac{2}{3}\).
Thus, the transformation rule can be described as: \[ (x, y) \to \left(\frac{2}{3}x, \frac{2}{3}y\right) \]
Out of the options provided, the correct rule is: \[ (x,y) \to \left(\frac{2}{3}x, \frac{2}{3}y\right) \]
So the correct answer is: \((x,y)→ (2/3 x, 2/3 y)\)