Question

an object is placed at point ( a=(3,-5,2) ). after a reflection over the ( xy )-plane, what are the coordinates of the new point ( a )? ( (-3,-5,-2) ) ( (3,5,-2) ) ( (3,-5,-2) ) ( (-3,5,2) )

Explanation:

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

When reflecting a point \((x,y,z)\) 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 point \(A=(3,-5,2)\)

For the point \(A=(3,-5,2)\), using the rule \((x,y,z)\to(x,y, - z)\), we substitute \(x = 3\), \(y=-5\), and \(z = 2\).
We get \(x'=3\), \(y'=-5\), and \(z'=-2\).

Answer:

\((3,-5,-2)\) (the third option)