Question

A figure has been dilated from the origin by a scale factor of
of. If another dilation from the origin maps the dilated image back
onto the original figure, what is its scale factor?

Answer 1

Answer:

See Explanation

Step-by-step explanation:

The question has missing details. So, I'll solve using a general assumption.

Let one of the coordinates of the figure be

$A = (x,y)$

Let the scale factor be n

When dilated, the new figure is:

$A' = n * A$

$A' = n * (x,y)$

To return the image back to the original figure, the new scale factor mus be a reciprocal of the previous scale factor i.e. $\frac{1}{n}$

So:

$A = A' * \frac{1}{n}$

Substitute n(x,y) for A';

$A = n(x,y) * \frac{1}{n}$

$A = \frac{n(x,y)}{n}$

$A = (x,y)$

Take for instance:

$A = (2,3)$

$n = 2$ -- scale factor

$A' = n * A$

$A' = 2 * (2,3)$

$A' = (4,6)$

To get A from A', using the analysis above

$A = \frac{1}{2} * (4,6)$

$A = (2,3)$