To determine whether the given statement is true or false, we need to consider the formula for the Euclidean distance between two points in a 2-dimensional plane.
Given two points, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], the Euclidean distance [tex]\(d\)[/tex] between them is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For our specific points, [tex]\((3,7)\)[/tex] and [tex]\((x_1, y_1)\)[/tex], let [tex]\(x_2 = 3\)[/tex] and [tex]\(y_2 = 7\)[/tex]. Substituting these values into the distance formula, we get:
[tex]\[ d = \sqrt{(x_1 - 3)^2 + (y_1 - 7)^2} \][/tex]
The given statement is:
"The distance between points [tex]\((3,7)\)[/tex] and [tex]\((x_1, y_1)\)[/tex] is the square root of [tex]\((x_1 - 3)^2 + (y_1 - 7)^2\)[/tex]."
Comparing this with our derived formula, we can see that they match exactly. Therefore, the statement provided is indeed true.
So the correct answer is:
A. True
