Question

What point is symmetric to the point $(-1,3,6)$ with respect to the $xy-$plane?

Short answer

The symmetric $xy-$plane point to the point$(-1,3,6)$is $(-1,3,-6).$

Step-by-step solution

Introduction.

It is symmetrical if the $y$and $x$values of a arithmetic formula can be swapped the line $y=x.$

Given Information.

Consider the following statement:

$(-1,3,6)$

The goal is to find the point on the $xy-$plane that is symmetric to this point.

Explanation.

Since the $y$and $z$coordinates are both positive and the $x$coordinate is negative, the point $(-1,3,6)$is in the fifth octant.

The point symmetric about the $xy-$plane to this point will be below the $xy-$plane with a negative $z$coordinate, which is the sixth octant.

In the sixth octant, the $x$and $y$coordinates are both negative, while the $y$coordinate is positive.

As an outcome, the point symmetric to the point $(-1,3,6)$about $xy-$plane is $(-1,3,-6).$