Question

find the distance from the point (0, 10, -9) to the origin. write your answer as a whole number or as a decimal rounded to the nearest hundredth.

Explanation:

Step1: Recall the distance formula in three - dimensions

The distance \(d\) between two points \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) is given by \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}\). The origin has coordinates \((0,0,0)\), and the given point is \((0,10, - 9)\). So, \(x_1 = 0,y_1 = 0,z_1 = 0,x_2 = 0,y_2 = 10,z_2=-9\).

Step2: Substitute the values into the formula

$$
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$$

Step3: Calculate the square - root

\(\sqrt{181}\approx13.45\) (rounded to the nearest hundredth)

Answer:

\(13.45\)