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Chapter 4: Problem 35

Graph each ordered pair. $$(-3,-5)$$

Short Answer

Expert verified
Plot the point (-3, -5) on the Cartesian plane by moving 3 units to the left of the origin along the x-axis and 5 units downward along the y-axis. Mark and label the point as (-3, -5).

Step by step solution

01

Understanding the Ordered Pair

An ordered pair is a pair of numbers written in the form (x, y), where x is the x-coordinate (horizontal coordinate) and y is the y-coordinate (vertical coordinate). In our case, the ordered pair is (-3, -5), meaning x = -3 and y = -5.
02

Plotting the Point on the Cartesian Plane

To plot the point (-3, -5) on the Cartesian plane, perform the following steps: 1. First, draw the Cartesian plane, which consists of a horizontal line (x-axis) and a vertical line (y-axis) that intersect in the middle. 2. Label the axes with positive and negative numbers, starting from 0 in the center (called the origin), and increasing as you move away from it. 3. Locate the point (-3, -5) by moving 3 units to the left of the origin along the x-axis (since x = -3) and 5 units downward along the y-axis (since y = -5). 4. Mark the point where these two positions intersect, labeling it as (-3, -5). Once you have plotted the point (-3, -5) on the Cartesian plane, you have graphed the given ordered pair.

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Key Concepts

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

Cartesian plane
The Cartesian plane is a two-dimensional plane defined by two perpendicular lines: the x-axis and the y-axis. This concept, introduced by Ren茅 Descartes, allows us to map out points using a pair of coordinates. The point where the x-axis and y-axis intersect is known as the origin, marked by the coordinate (0, 0). The Cartesian plane is divided into four quadrants, each helping to determine the sign of the x and y values for any given point. The top right quadrant contains positive x and y values, moving counterclockwise, the signs change accordingly.
plotting points
Plotting points on a Cartesian plane involves identifying a location using an ordered pair, (x, y). This ordered pair tells you exactly where to place your point along the axes. Begin by finding the x-coordinate, which shows your horizontal movement from the origin. Next, use the y-coordinate for vertical placement. Together, these coordinates give a precise location on the plane. For example, a point like (-3, -5) means moving 3 units left along the x-axis and 5 units down along the y-axis. Be mindful of the direction, as negative and positive values will guide where your point should go.
x-axis and y-axis
The x-axis and y-axis are the backbone of the Cartesian coordinate system. The x-axis is the horizontal line that extends infinitely in both directions, marked as positive to the right and negative to the left. The y-axis is the vertical counterpart, with positive values extending upwards and negative values downwards. Each axis acts like a number line and helps in plotting exact locations on the plane. Understanding these axes is essential for determining where points need to be placed, based on their given coordinates.
coordinate system
A coordinate system is a standardized method used to define locations on a plane. It allows us to express points accurately using a set of values, typically noted as (x, y) in the Cartesian system. This system is pivotal in mathematics and helps bridge abstract concepts with visual representation. Each ordered pair you encounter corresponds to a specific point. Understanding the coordinate system is key to mastering topics like geometry, algebra, and even computer graphics. It provides a universal way to visualize and interpret spatial relationships.

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Most popular questions from this chapter

Graph each function by making a table of values and plotting points. $$g(x)=-\frac{3}{5} x+2$$

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