Question

find the distance from the point (-4, 7, 0) 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 3D

The distance formula between two points \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}\). The origin is \((0,0,0)\), and the given point is \((-4,7,0)\).

Step2: Substitute values into the formula

Substitute \(x_1=-4,y_1 = 7,z_1=0,x_2 = 0,y_2=0,z_2=0\) into the formula: \(d=\sqrt{(0-(-4))^2+(0 - 7)^2+(0 - 0)^2}=\sqrt{4^2+(-7)^2+0^2}\).

Step3: Calculate the squares

\(4^2=16\), \((-7)^2 = 49\), \(0^2=0\). So \(d=\sqrt{16 + 49+0}=\sqrt{65}\).

Step4: Evaluate the square - root

\(\sqrt{65}\approx8.06\) (rounded to the nearest hundredth).

Answer:

\(8.06\)