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 point that  is symmetric to the point \((−1, 3, 6)\) with

respect to the XY-plane is \((-1,3,-6)\). 

Step 1. Given Information

The given point is  \((−1, 3, 6)\)

Here, the x coordinate is positive, and both the y and z coordinates are negative. Thus, the given point lies in the fifth octant.

Step 2. Finding the symmetric point.

As the given point lies in the fifth octant, its symmetric point about XY-plane lies in the sixth octant where both the x and z coordinates are negative and the y-coordinate is positive.

Therefore, the point that  is symmetric to the point \((−1, 3, 6)\) with

respect to the XY-plane is \((-1,3,-6)\)