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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. R - Algebra ReviewProblema 35c
Capitolo 1, Problema 35c

Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (c) origin. (-4, -2)

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Identify the given point as \((-4, -2)\) on the Cartesian coordinate plane.
Recall that the point symmetric to a given point with respect to the origin is found by negating both the \(x\) and \(y\) coordinates of the original point.
Apply this rule to the point \((-4, -2)\): the symmetric point with respect to the origin will be \((4, 2)\).
Plot the original point \((-4, -2)\) on the coordinate plane by moving 4 units left and 2 units down from the origin.
Plot the symmetric point \((4, 2)\) by moving 4 units right and 2 units up from the origin.

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Concetti chiave

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Coordinate Plane and Plotting Points

The coordinate plane is a two-dimensional surface defined by the x-axis (horizontal) and y-axis (vertical). Each point is represented by an ordered pair (x, y), where x indicates horizontal position and y indicates vertical position. Plotting a point involves locating its position based on these coordinates.
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Convert Points from Polar to Rectangular

Symmetry with Respect to the Origin

Symmetry about the origin means that for any point (x, y), its symmetric point is (-x, -y). This reflects the point through the origin, effectively rotating it 180 degrees around (0,0). It is a key concept in understanding transformations in the coordinate plane.
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Even and Odd Identities

Reflection and Transformation in the Coordinate Plane

Reflection is a transformation producing a mirror image of a point or shape across a specific line or point. Reflecting a point about the origin is a specific transformation that changes (x, y) to (-x, -y), helping analyze geometric properties and symmetries.
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Reflections of Functions
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Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (a) x-axis (-4, -2)

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For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.

y = |x - 2|

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