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Chapter 1: Problem 63

Explain why \((5,-2)\) and \((-2,5)\) do not represent the same point.

Short Answer

Expert verified
The points (5,-2) and (-2,5) do not represent the same point because they are located in different positions on the coordinate plane and hence they belong to different quadrants.

Step by step solution

01

Understanding the Coordinates

Let's first understand that a coordinate, represented by an ordered pair (x, y), shows a specific location on a coordinate plane. The x-value (first number) describes the horizontal position and the y-value (second number) describes the vertical position. If we swap these two numbers, we are essentially swapping the vertical and horizontal positions which results in a different point on the plane.
02

Applying the concept

The ordered pair (5,-2) represents a point on the plane that is 5 units to the right along the x-axis (because it's positive) and 2 units below the x-axis (since it's negative). On the other hand, the ordered pair (-2,5) is 2 units to the left of origin (because it's negative) along the x-axis and 5 units above the x-axis (because it's positive).
03

Concluding the difference

Consequently, the points (5,-2) and (-2,5) are located in different quadrants and thus they cannot be the same.

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