Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What is the center of the circle that has a diameter whose endpoints are [tex]\((2, 7)\)[/tex] and [tex]\((-6, -1)\)[/tex]?

Sagot :

To find the center of a circle given the endpoints of its diameter, we need to determine the midpoint of the segment connecting these two endpoints.

Let's denote the endpoints of the diameter as [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]. Specifically, we have:
[tex]\[ (x_1, y_1) = (2, 7) \][/tex]
[tex]\[ (x_2, y_2) = (-6, -1) \][/tex]

The formula for the midpoint [tex]\((x_m, y_m)\)[/tex] of a segment connecting points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ x_m = \frac{x_1 + x_2}{2} \][/tex]
[tex]\[ y_m = \frac{y_1 + y_2}{2} \][/tex]

First, we compute the x-coordinate of the midpoint:
[tex]\[ x_m = \frac{2 + (-6)}{2} \][/tex]
[tex]\[ x_m = \frac{2 - 6}{2} \][/tex]
[tex]\[ x_m = \frac{-4}{2} \][/tex]
[tex]\[ x_m = -2 \][/tex]

Next, we compute the y-coordinate of the midpoint:
[tex]\[ y_m = \frac{7 + (-1)}{2} \][/tex]
[tex]\[ y_m = \frac{7 - 1}{2} \][/tex]
[tex]\[ y_m = \frac{6}{2} \][/tex]
[tex]\[ y_m = 3 \][/tex]

Therefore, the center of the circle, which is the midpoint of the diameter, is:
[tex]\[ (-2, 3) \][/tex]

This point [tex]\((-2, 3)\)[/tex] is the center of the circle that has a diameter with endpoints [tex]\((2, 7)\)[/tex] and [tex]\((-6, -1)\)[/tex].
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.