Question

question 5 of 10
opposite points on the diameter of a hula - hoop are given by the coordinates a (-15, 36) and b (100, -18).
approximately what length (circumference) of plastic is needed to manufacture this hula - hoop? note that all measurements are in centimetres.

Explanation:

Step1: Calculate diameter length

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $(x_1,y_1)=(-15,36)$ and $(x_2,y_2)=(100,-18)$.
$d=\sqrt{(100 + 15)^2+(-18 - 36)^2}=\sqrt{115^2+(-54)^2}=\sqrt{13225 + 2916}=\sqrt{16141}\approx127$

Step2: Calculate circumference

Use formula $C=\pi d$. Substitute $d\approx127$.
$C\approx3.14\times127 = 398.78\approx399$

Answer:

399 centimetres