Chapter 9.2, Problem 1AYU

To determine

To fill: Point of symmetric with respect to the origin if the rectangular coordinates of a point $\left(4, - 6\right)$.

Answer to Problem 1AYU

Solution:

The required point is $\left(- 4, 6\right)$.

Given:

Point of rectangular coordinates is $\left(4, - 6\right)$. Need to find the symmetric point with respect to the origin.

Explanation of Solution

A graph is said to be symmetric with respect to the origin if, for every point $\left(x, y\right)$ on the graph, the point $\left(- x, - y\right)$ is also on the graph.

By the definition of symmetry, for the point $\left(4, - 6\right)$ on the rectangular coordinate, the point $\left(- 4, - \left(- 6\right)\right)$ is also on the rectangular coordinates.

The required point is $\left(- 4, 6\right)$.