Transverse intersection of submanifolds of $\mathbb P^2$

Question

Denote $[x_0:x_1:x_2]$ points in $\mathbb P^2$. Let $M=V(x_0x_1)$ the vanishing set of $x_0x_1$, $N=V(x_0x_2)$. Then $M\bigcap N=V(x_0)\bigcup \{[1:0:0]\}$. I can see the intersection is transverse at the point $[1:0:0]$. But is it transverse on the line $V(x_0)$?