Direct sum $\mathbb R^2$ and projection maps

Question

Really struggling with these types of questions and my past papers don't have answers, any help would be greatly appreciated!

Let $X = \{(x,0):x \in \mathbb R\}$ and $D= \{(x,x):x\in \mathbb R\}$

How would I prove that the direct sum of $X$ and $D$ are equal to $\mathbb R^2$?

Answer 1

We have $(x,y)=(x-y,0)+(y,y)$. Hence $\mathbb R^2=X+D$.

Its your turn to show that $ X \cap D=\{(0,0)\}$