Question

a sensor is initially placed at coordinates $(2, - 1, 5)$. it is then translated 4 units in the positive x direction, 2 units in the negative y direction, and 3 units in the positive z direction. what are the new coordinates of the sensor? $(6,1,2)$ $(5, - 6,6)$ $(-2, - 3,2)$ $(6, - 3,8)$

Explanation:

Step1: Calculate new x - coordinate

The initial x - coordinate is \(2\). Translating \(4\) units in the positive x - direction: \(2 + 4=6\)

Step2: Calculate new y - coordinate

The initial y - coordinate is \(-1\). Translating \(2\) units in the negative y - direction: \(-1-2=-3\)

Step3: Calculate new z - coordinate

The initial z - coordinate is \(5\). Translating \(3\) units in the positive z - direction: \(5 + 3=8\)

Answer:

\((6,-3,8)\) (the fourth option)