Final answer:
To reverse a dilation with a scale factor of 7/5, perform another dilation with the reciprocal scale factor of 5/7.
This will bring the original distances back to their initial values, effectively undoing the initial dilation.
Step-by-step explanation:
The reciprocal of 7/5 is 5/7, meaning that a dilation with center O and a scale factor of 5/7 will undo the original dilation.
The reason for this is that when you apply a dilation with a certain scale factor, you are essentially multiplying the original distances from the center of dilation by that factor.
To reverse this, you want to multiply by a factor that will bring you back to the original distances.
Multiplying by the reciprocal does exactly this because the product of a number and its reciprocal is 1, effectively canceling out the original dilation.
For example, if a point was originally 10 units away from center O and was dilated by a factor of 7/5, it would be 14 units away after the transformation (10 * 7/5 = 14).
To reverse this, we multiply 14 by 5/7 to get back to the original 10 units (14 * 5/7 = 10).