Question

find the distance from the point (-2, -1, -7) 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 \( d=\sqrt{x^{2}+y^{2}+z^{2}} \). For the point \( (-2, -1, -7) \), \( x = - 2 \), \( y=-1 \), \( z = - 7 \).

Step2: Substitute values into formula

Substitute \( x=-2 \), \( y = - 1 \), \( z=-7 \) into the formula: \( d=\sqrt{(-2)^{2}+(-1)^{2}+(-7)^{2}} \). Calculate each square: \( (-2)^{2}=4 \), \( (-1)^{2}=1 \), \( (-7)^{2}=49 \). Then sum them: \( 4 + 1+49=54 \). So \( d=\sqrt{54} \).

Step3: Calculate the square root

\( \sqrt{54}\approx7.35 \) (rounded to the nearest hundredth).

Answer:

\( 7.35 \)