Question

A circle has a diameter with endpoints A(-4,4) and B(2.-3). What is the length of the diameter?

Answer 1

`\sqrt[]{85}`

Step-by-step explanation

The diameter of the circle has endpoints:

A(-4, 4) and B(2, -3)

To find the length of the diameter, we have to find the distance between the two endpoints of the diameter.

We use the formula:

`D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Where (x1, y1) = (-4, 4)

(x2, y2) = (2, -3)

Therefore, the length of the diameter is:

`\begin{gathered} D\text{ = }\sqrt[]{(2-(-4))^2+(-3-4)^2} \\ D\text{ = }\sqrt[]{(2+4)^2+(-7)^2}\text{ = }\sqrt[]{6^2+(-7)^2} \\ D\text{ = }\sqrt[]{36\text{ + 49}}\text{ = }\sqrt[]{85} \\ D\text{ = }9.22\text{ or }\sqrt[]{85} \end{gathered}`

The length of the diameter is 9.22