Answer :
Let's analyze the given problem step by step.
The distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a Cartesian plane is given by the Euclidean distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For the specific points in the question:
- [tex]\((x_1, y_1)\)[/tex] is a general point.
- [tex]\((3, 7)\)[/tex] is a specific point.
Substituting these points into the distance formula, we get:
[tex]\[ d = \sqrt{(x_1 - 3)^2 + (y_1 - 7)^2} \][/tex]
This matches exactly with what is given in the problem statement:
"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]."
Since the Euclidean distance formula is correctly described by the given statement, the answer is:
A. True
The distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a Cartesian plane is given by the Euclidean distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For the specific points in the question:
- [tex]\((x_1, y_1)\)[/tex] is a general point.
- [tex]\((3, 7)\)[/tex] is a specific point.
Substituting these points into the distance formula, we get:
[tex]\[ d = \sqrt{(x_1 - 3)^2 + (y_1 - 7)^2} \][/tex]
This matches exactly with what is given in the problem statement:
"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]."
Since the Euclidean distance formula is correctly described by the given statement, the answer is:
A. True
