Q. 12 - Calculus

Question

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

Step-by-Step Solution

Answer

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

Step1: Introduction.

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

Step2: 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.

Step3: 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 $(-1,3,-6).$