ANSWER
[tex]\sqrt[]{85}[/tex]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:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where (x1, y1) = (-4, 4)
(x2, y2) = (2, -3)
Therefore, the length of the diameter is:
[tex]\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}[/tex]The length of the diameter is 9.22
