Is this definition of distance between two points correct?

Question

I came across this definition

but it's confusing to me.

Shouldn't $A$ be $(x_1,y_1)$ instead of $(x_1,x_2)$? Same for $Y$. And even if $A$ was correct like that then shouldn't the formula for the distance be written as $$d(X,Y) =\sqrt{(y_1-x_1)^2+(y_2-x_2)^2}$$

What am I getting wrong?

Answer 1

Indeed there is a typo and your expression

$$d(X,Y) =\sqrt{(y_1-x_1)^2+(y_2-x_2)^2}$$

is the correct one by direct application of pythagorean theorem.