Solution:
The rule for y-axis reflection is (x,y)⟶(−x,y), thus reflection in the y-axis, the x is negated.
⇒(−2,3) reflected in the y-axis will be −(−2),3 but −−=+, hence (2,3)
A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage.
A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
Some simple reflections can be performed easily in the coordinate plane using the general rules below.
Reflection in the x-axis:
A reflection of a point over the x-axis is shown.
The rule for a reflection over the x-axis is (x,y)⟶(x,−y), thus reflection in the x-axis, the y is negated.
Reflection in the y-axis:
A reflection of a point over the y-axis is shown.
The rule for a reflection over the y-axis is (x,y)⟶(−x,y), thus reflection in the y-axis, the x is negated.
Reflection in the line y=x :
A reflection of a point over the line y=x is shown.
The rule for a reflection in the line y=x is (x,y)⟶(y,x), thus you simply switch their positions.
Reflection in the line y=−x :
A reflection of a point over the line y=−x is shown.
The rule for a reflection in the origin is (x,y)⟶(−y,−x), thus you simply negate the result of y=x.
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