Q.5 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

What point is symmetric with respect to the $y-$axis to the point $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$.

Step-by-Step Solution

Answer

The point that is symmetric with respect to the $y-$axis to the point $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$ is$\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)$.

Given information

Consider the point $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$.

The main objective is to find the point that is symmetric with respect to $y-$axis to the point $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$.

Evaluate

According to the property of the symmetric with respect to $y$, for a point $\left(x,y\right)$, the point that is symmetric with respect to $y-$axis is $\left(-x,y\right)$.

So, the point that is sysmmetric with respect to $y-$axis to the point $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$ is $\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)$.