Question

a robots initial position is ( p(-3,8,-5) ). its new position is reflected over the ( xy - ) plane. what are its new coordinates, ( r )? ( (-3,-8,-5) ) ( (3,8,5) ) ( (3,8,-5) ) ( (-3,8,5) )

Explanation:

Step1: Recall the reflection rule over the \(xy -\)plane

When a point \((x,y,z)\) is reflected over the \(xy -\)plane, the \(x\) and \(y\) coordinates remain the same, and the \(z\) - coordinate changes its sign. The rule is \((x,y,z)\to(x,y, - z)\)

Step2: Apply the rule to the given point \(P(-3,8,-5)\)

Here \(x=-3\), \(y = 8\), and \(z=-5\). Using the reflection rule \((x,y,z)\to(x,y, - z)\), we substitute \(z=-5\) into \(-z\). So \(-z=-(-5) = 5\)

Answer:

\((-3,8,5)\) (the fourth option)