Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

The distance between the 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].

A. True
B. False


Sagot :

To determine if the statement is true or false, let’s use the Euclidean distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a plane. The Euclidean distance [tex]\(d\)[/tex] is given by:

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

In this problem, we have the points [tex]\((x_1, y_1)\)[/tex] and [tex]\((3, 7)\)[/tex]. So, [tex]\(x_2 = 3\)[/tex] and [tex]\(y_2 = 7\)[/tex]. Plugging these into the distance formula, we get:

[tex]\[ d = \sqrt{(3 - x_1)^2 + (7 - y_1)^2} \][/tex]

To simplify, consider:

[tex]\[ (3 - x_1)^2 = (x_1 - 3)^2 \][/tex]
[tex]\[ (7 - y_1)^2 = (y_1 - 7)^2 \][/tex]

So, we can rewrite the distance as:

[tex]\[ d = \sqrt{(x_1 - 3)^2 + (y_1 - 7)^2} \][/tex]

The statement given is that the distance between the points [tex]\((3, 7)\)[/tex] and [tex]\((x_1, y_1)\)[/tex] is:

[tex]\[ \sqrt{(x_1-3)^2+(y_1-7)^2} \][/tex]

This matches the Euclidean distance formula derived above. Hence, the statement is:

A. True