Reflections

Reflect points over axes and common lines.

Lesson 2 of 53 parts Practice Flashcards

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Reflection over Coordinate Axes

Objective: Reflect a point over x- or y-axis.

Across the x-axis: (x,y)→(x,−y). Across the y-axis: (x,y)→(−x,y).

Triangle ABC in quadrant I is reflected over the y-axis (red) and over the x-axis (gold).

Formulas

$x-axis: (x,y) → (x,−y)$
$y-axis: (x,y) → (−x,y)$

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Reflection over Coordinate Axes

Objective: Reflect a point over x- or y-axis.

Across the x-axis: (x,y)→(x,−y). Across the y-axis: (x,y)→(−x,y).

Formulas

$x-axis: (x,y) → (x,−y)$
$y-axis: (x,y) → (−x,y)$

Reflection over y=x and y=−x

Objective: Apply diagonal-line reflection rules.

Across y=x, (x,y)→(y,x); across y=−x, (x,y)→(−y,−x).

P(1, 4) reflects over y = x to (4, 1) and over y = −x to (−4, −1).

Reflection Properties

Objective: Recognize the mirror line and reversed orientation.

A reflection is a rigid motion. The reflection line is the perpendicular bisector of each segment connecting a point to its image, unless the point is on that line. Orientation reverses.

Point P and image P′ are equidistant from the reflection line, which meets PP′ at a right angle; the mirrored triangle has reversed orientation.

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