Question

What is the image point of (5,-6)(5,−6) after the transformation r_{\text{y-axis}}\circ T_{-4,0}r

Answer 1

The image point of P(x,y) = (5, -6) after applying a horizontal reflection is P'(x,y) = (1, -6).

How to apply a rigid transformation in a point on a Cartesian plane

In geometry, a rigid transformation is a transformation applied onto a geometric object such that Euclidean distance in every point of it is conserved. Translations are examples of rigid transformations and are defined by this formula:

P'(x,y) = P(x,y) + T(x,y)   (1)

Where:

• P(x,y) - Original point
• T(x,y) - Translation vector
• P'(x,y) - Image point

If we know that P(x,y) = (5, -6) and T(x,y) = (-4, 0), then the image point is:

P'(x,y) = (5, -6) + (-4, 0)

P'(x,y) = (1, -6)

The image point of P(x,y) = (5, -6) after applying a horizontal reflection is P'(x,y) = (1, -6). $\blacksquare$

Remark

Statement is incorrect and poorly formatted. Correct form is shown below:

What is the image point of (x, y) = (5, -6) after the transformation of translating horizontally the point -4 units to the y-axis?

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