Problem 665

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

 

Solution:-

 

Recall  for any point (x,y), the point symmetric about the y-axis to (x,y) is the point (-x,y).

 

If two point are symmetric about the y-axis, then the point have the same y-coordinate and opposite x-coordinates. Replace the x-coordinate of the given point with its opposite.

 

Identify the x-coordinate of the given point(  \frac{\sqrt{3}}{2} ,\frac{-1}{2}).

 

X = \frac{\sqrt{3}}{2}

If x = \frac{\sqrt{3}}{2}, than the opposite of x, -x, = –\frac{\sqrt{3}}{2}.

Therefore , the point symmetric to the point (  \frac{\sqrt{3}}{2} ,\frac{-1}{2}) with respect to the y-axis is (  \frac{-\sqrt{3}}{2} ,\frac{-1}{2})

 

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