Covering compact convex $-C \subseteq \mathbb{R}^d$ with $x+dC$ for some $x \in \mathbb{R}^d$: counterexample?

Question

From Matousek's Lectures in Discrete Geometry:

Let $C$ be compact convex in $\mathbb{R}^d$. Prove that there is a suitable translation of $C$ blown up by a factor of $d$ which covers the reflection of $C$; that is, show there is an $x \in \mathbb{R}^d$ such that $-C \subseteq x + dC$.

I am confused by this question. Consider the following:

Then the reflection of this $C$ will be oriented in a different direction than $C$, and I don't see how it blown up by a factor of $2$ will make it able to cover $-C$. The greatest vertical distance between points in $2C$ is $20$, while the greatest vertical distance of between two points in $-C$ is $110$.

Am I misunderstanding the question? Or is this a counterexample?

Answer 1

I'm not sure why you think that the greatest vertical distance between two points in $-C$ is $110$; it should just be $10$, same as $C$.

Here is a diagram showing a scaled copy of $C$ overlaid on $-C$: