44. Right-triangle Delta RST will be rotnted about the x-axis to form a right cinenlar conc. How long in coordinate units, is the radius of the cono's base? R G. 3 H. J.6 K. 9

To find the radius of the cone's base, we need to determine the length of the shorter leg of the right triangle $\Delta RST$.<br /><br />Given that the triangle is reflected about the x-axis, the coordinates of the vertices will change as follows:<br />- R(-3, 0) will become R'(-3, 0)<br />- S(0, 3) will become S'(0, -3)<br />- T(3, 0) will become T'(3, 0)<br /><br />Now, we can use the distance formula to find the length of the shorter leg of the triangle:<br />Distance between R' and S' = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$<br />Distance between R' and S' = $\sqrt{(0 - (-3))^2 + (-3 - 0)^2}$<br />Distance between R S' = $\sqrt{3^2 + (-3)^2}$<br />Distance between R' and S' = $\sqrt{9 + 9}$<br />Distance between R' and S' = $\sqrt{18}$<br />Distance between R' and S' = $3\sqrt{2}$<br /><br />Therefore, the radius of the cone's base is $3\sqrt{2}$ coordinate units.<br /><br />Answer: G. 3