Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem 33b

Chapter 1, Problem 33b

Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (b) y-axis (5, -3)

Verified step by step guidance

Identify the given point as \((5, -3)\), where \(5\) is the \(x\)-coordinate and \(-3\) is the \(y\)-coordinate.

Recall that symmetry with respect to the \(y\)-axis means reflecting the point across the \(y\)-axis. This changes the sign of the \(x\)-coordinate but keeps the \(y\)-coordinate the same.

Apply the reflection rule: For a point \((x, y)\), its symmetric point with respect to the \(y\)-axis is \((-x, y)\).

Using this rule, find the symmetric point of \((5, -3)\) by changing the \(x\)-coordinate from \(5\) to \(-5\), while keeping the \(y\)-coordinate \(-3\) unchanged. So, the symmetric point is \((-5, -3)\).

Plot both points on the coordinate plane: the original point \((5, -3)\) on the right side of the \(y\)-axis, and the symmetric point \((-5, -3)\) on the left side, at the same vertical level.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Symmetry with Respect to the y-Axis

Symmetry about the y-axis means that for any point (x, y), its symmetric point has coordinates (-x, y). This reflects the point across the vertical y-axis, changing the sign of the x-coordinate while keeping the y-coordinate the same.

Reflection of Points in the Coordinate Plane

Reflection involves creating a mirror image of a point across a specific axis. For the y-axis, reflection changes the x-coordinate's sign but leaves the y-coordinate unchanged. Understanding reflections helps in visualizing geometric transformations and solving related problems.

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Related Practice

Textbook Question

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. (5, -3)

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Textbook Question

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 (5, -3)

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Textbook Question

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Irrational numbers

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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 - 3)

Textbook Question

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Real numbers