To determine whether the statement is true, let's recall the formula for the distance between two points in a two-dimensional plane [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]. The distance [tex]\(d\)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Now, let's apply this formula for the specific points [tex]\((1, 2)\)[/tex] and [tex]\((x_1, y_1)\)[/tex].
Substituting [tex]\((x_2, y_2) = (1, 2)\)[/tex] and [tex]\((x_1, y_1)\)[/tex] remains as [tex]\((x_1, y_1)\)[/tex], the distance [tex]\(d\)[/tex] becomes:
[tex]\[ d = \sqrt{(x_1 - 1)^2 + (y_1 - 2)^2} \][/tex]
The given statement says that the distance between the points [tex]\((1,2)\)[/tex] and [tex]\((x_1, y_1)\)[/tex] is the square root of [tex]\((x_1 - 1)^2 + (y_1 - 2)^2\)[/tex]. This matches our derived formula.
Therefore, the given statement is:
A. True
