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Chapter 11: Problem 4

The point symmetric with respect to the \(y\) -axis to the point (-2,5) is _____

Short Answer

Expert verified
(2, 5)

Step by step solution

01

Understand Symmetry with respect to the y-axis

Symmetry with respect to the y-axis means that each point \((x, y)\) is mapped to the point \((-x, y)\).
02

Identify Original Point Coordinates

The original coordinates given are \((-2, 5)\).
03

Apply Symmetry Rule

Following the rule for symmetry with respect to the y-axis, change the x-coordinate from \(-2\) to \(+2\) while keeping the y-coordinate the same. This results in the new point \(2, 5)\).
04

Write the Symmetric Point

Thus, the point symmetric with respect to the y-axis to the point \((-2, 5)\) is \(2, 5)\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

y-axis symmetry
When we talk about y-axis symmetry in coordinate geometry, we mean that a point and its symmetric counterpart are mirror images across the y-axis. Imagine folding your graph paper along the y-axis. The points that match up on each side are symmetric. To find the symmetric point of any given point \((x, y)\) with respect to the y-axis, you simply reverse the sign of the x-coordinate. The new coordinates will be \((-x, y)\). We keep the y-coordinate the same because we are just reflecting horizontally. For example, if you have the point \((-2, 5)\), its symmetric point across the y-axis would be \((2, 5)\).
coordinates
Coordinates are ordered pairs that indicate the position of a point on a plane. They are written as \((x, y)\), where \('x'\) represents the horizontal position and \('y'\) represents the vertical position. Coordinates help us easily locate points on a graph or map. For example, the point \((-2, 5)\) is located 2 units to the left of the y-axis and 5 units above the x-axis. When dealing with symmetry, understanding coordinates is crucial because we manipulate these values to find symmetric points.
mapping points
Mapping points in coordinate geometry refers to plotting and transforming points on a plane. When considering symmetry, mapping points involves applying specific rules to find corresponding points. For y-axis symmetry, we transform the point \((x, y)\) to \((-x, y)\). This process does not change the y-coordinate, as it only mirrors the point across the y-axis. If you start with the point \((-2, 5)\) and apply the mirroring rule, you end up with the new coordinates \((2, 5)\). Mapping points accurately is essential in visualizing and solving geometric problems.

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