To determine whether the statement about the distance between the points [tex]\((1, 2)\)[/tex] and [tex]\((x_1, y_1)\)[/tex] is correct, we need to consider the formula for the Euclidean distance between two points in a 2-dimensional plane.
The formula for the distance [tex]\(d\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, the coordinates of the first point are [tex]\((1, 2)\)[/tex], so [tex]\(x_2 = 1\)[/tex] and [tex]\(y_2 = 2\)[/tex]. The coordinates of the second point are [tex]\((x_1, y_1)\)[/tex].
Substituting these points into the distance formula:
[tex]\[ d = \sqrt{(x_1 - 1)^2 + (y_1 - 2)^2} \][/tex]
This matches exactly with the given expression:
[tex]\[ \sqrt{(x_1 - 1)^2 + (y_1 - 2)^2} \][/tex]
Since the given formula correctly represents the Euclidean distance between the two points [tex]\((1, 2)\)[/tex] and [tex]\((x_1, y_1)\)[/tex], the statement is true.
Therefore, the answer is:
A. True
