Q. 11

What point is symmetric about the origin to the point $(5, - 6, 7) ?$

Verified

Answer

The symmetric point to the origin $(5, - 6, 7)$ is $(- 5, 6, - 7) .$

1Step1: Introduction.

If $(a, b)$ and $(- a, - b)$ are on a graph, it is said to be symmetric about the origin.

2Step2: Given Information.

Consider the following statement:

$(5, - 6, 7)$

The goal is to find this same point about origin that really is symmetric to this point.

3Step3: Explanation.

Because the $x$ and $z$ coordinates are positive and the $y$ coordinate is negative, the point $(5, - 6, 7)$ is in the third octant.

The symmetric point well about origin to this juncture will be in the sixth octant.

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

As a result, the point symmetric to a point $(5, - 6, 7)$ about origin is $(- 5, 6, - 7) .$