NotThatSmart

This problem is not as hard as it might seem!

We have

\((1 + 1.5)^2  = (2.5)^2  = 6.25\)

So 6.25 is our answer. 

Thanks! :)

First, let's note that XZW  will form a triangle

From the problem, we have that 

\(\angle ZXW  = 90^\circ \\ \angle XWZ = 60^\circ\)

Thus, we can easily find XZW since it's the last angle in the triangle. 

So \(\angle XZW =  180 - 90 - 60  =   30^\circ\)

Thanks! :)

Look at the graph attached below. 

The ray will strike X and then, because angle A = angle B  it will travel to vertex D

Thus, the total path legnth is 

\(2 \sqrt {0 .5^2  + 1^2 } =  2 \sqrt { 5/4}  = \sqrt 5\)

Thanks! :)

This question isn't hard at all, and only involves one key fact. 

First, we HAVE to know the formula 

Dilation Factor = Length of Image / Length of Pre-image

So, now, we just plug in some numbers and we are done!

Length of AB (image) = 30 units

\(5 = 30 / OA\\ OA = 30/5\\ OA = 6\)

So OA is basically just 6 units. 

Thanks! :)