The <em>image</em> point of <em>P(x,y) =</em><em> (5, -6)</em> after applying a <em>horizontal</em> reflection is <em>P'(x,y) =</em><em> (1, -6)</em>.
<h3>
How to apply a rigid transformation in a point on a Cartesian plane</h3>
In geometry, a <em>rigid</em> transformation is a transformation applied onto a <em>geometric</em> object such that <em>Euclidean</em> distance in every point of it is conserved. Translations are examples of <em>rigid</em> transformations and are defined by this formula:
<em>P'(x,y) = P(x,y) + T(x,y)</em> (1)
Where:
- <em>P(x,y)</em> - Original point
- <em>T(x,y)</em> - Translation vector
- <em>P'(x,y)</em> - Image point
If we know that <em>P(x,y)</em><em> = (5, -6)</em> and <em>T(x,y)</em><em> = (-4, 0)</em>, then the image point is:
<em>P'(x,y) = (5, -6) + (-4, 0)</em>
<em>P'(x,y) = (1, -6)</em>
The <em>image</em> point of <em>P(x,y) =</em><em> (5, -6)</em> after applying a <em>horizontal</em> reflection is <em>P'(x,y) =</em><em> (1, -6)</em>. 
<h3>Remark</h3>
Statement is incorrect and poorly formatted. Correct form is shown below:
<em>What is the image point of </em><em>(x, y) = (5, -6)</em><em> after the transformation of translating horizontally the point -4 units to the y-axis?</em>
To learn more on rigid transformations, we kindly invite to check this verified question: brainly.com/question/1761538