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 3D distance formula

The distance \( d \) between a point \( (x, y, z) \) and the origin \( (0, 0, 0) \) is given by \( d=\sqrt{x^{2}+y^{2}+z^{2}} \). Here, \( x = 0 \), \( y = 10 \), \( z=-9 \).

Step2: Substitute values into formula

Substitute \( x = 0 \), \( y = 10 \), \( z = - 9 \) into the formula: \( d=\sqrt{0^{2}+10^{2}+(-9)^{2}}=\sqrt{0 + 100+81}=\sqrt{181} \).

Step3: Calculate the square root

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

Answer:

13.45