Question

Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'. If R'S' is 2 units, what is RS?

A.
4 units
B.
2 units
C.
0.5 units
D.
1 unit
Reset
Next

Answer 1

Answer: A.4 units

Explanation:

We know that if a figure is dilated by a scale factor of k , then the measure of the corresponding image (l') of a line segment having measure 'l' is given by :-

`l'=kl`

Given : Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'.

The measure of line segment R'S' = 2 units

The scale factor :
`k=(1)/(2)`

Using the above equation , we have

`R'S'=(1)/(2)RS\\\\\Rightarrow\ RS= 2* R'S'\\\\\Rightarrow\ RS= 2*2=4`

Hence, RS = 4 units.