Find $k$ (slope) if there's a homothety centered at origin with $k$ coefficient and it moves point $A(2;3)$ to point $B(2x-1;x)$

Question

Find $k$ (slope) if there's a homothety centered at origin with $k$ coefficient and it moves point $A(2;3)$ to point $B(2x-1;x)$

First I did this $\frac{2}3=\frac{2x-1}x$ to find $x$, I got $x=\frac{3}4$

Then I put $x$ in second points to get exact value, got $B = (\frac{1}2;\frac{3}4)$

Then I just did $\frac{y_2-y_1}{x_2-x_1}$ to find slope, got to $k=\frac{3}2$.

It's the wrong answer though it made sense to me, How should I do it correctly?

Answer 1

Yes you did it fine.

You could get a slope immediately since an origin $(0,0)$ and $A(2,3)$ determine that slope.