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Chapter 9: Problem 29

Short Response Graph point \(M\) with coordinates \((-4,-3)\). (Lesson 2-4)

Short Answer

Expert verified
Plot point M at (-4, -3) on the graph by moving 4 units left and 3 units down from the origin.

Step by step solution

01

Understand the Coordinate System

The coordinate system consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Points are plotted using coordinates in the form \(x, y\). The first number \(x\) is the horizontal position, and the second number \(y\) is the vertical position.
02

Identify the Coordinates of Point M

Point M has coordinates \((-4, -3)\). This means that the x-coordinate is -4, and the y-coordinate is -3, indicating the point's position on the graph.
03

Locate the X-Coordinate on the Graph

Starting from the origin (0,0), move 4 units to the left along the x-axis because the x-coordinate is -4.
04

Locate the Y-Coordinate on the Graph

From the point \((-4, 0)\), move 3 units down along the y-axis to reach \((-4, -3)\) as the y-coordinate is -3.
05

Plot Point M

Place a dot at the intersection of the x-coordinate -4 and the y-coordinate -3 on the graph. This exact point represents M in the coordinate plane.

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Key Concepts

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

Plotting Points
Plotting points in a coordinate system is one of the fundamental skills in graphing. When you receive a pair of coordinates like \((-4, -3)\), the first thing you need to do is understand what each number represents. In a coordinate pair, the first number is the x-coordinate and the second number is the y-coordinate. This tells you:
  • Where to move horizontally on the graph (left or right).
  • Where to move vertically on the graph (up or down).
Think of plotting as following a map: the x-coordinate tells you how far to travel east or west, while the y-coordinate shows you how far to go north or south. By placing a point where these coordinates intersect, you can accurately plot any point on the graph.
X-axis
The x-axis is a crucial part of the coordinate system. Imagine a horizontal line that stretches from left to right across a graph. This is your x-axis. The center of this axis is known as the origin (0,0). From this point:
  • Positive x-values are located to the right. If you have a number like +3, you move 3 units to the right from the origin.
  • Negative x-values are positioned to the left. For -4, you would move 4 units left from the origin, as happens with point M \((-4, -3)\).
In practice, always start at the origin and move horizontally according to your x-coordinate. This step is vital for accurately locating any point's initial position on the graph.
Y-axis
The y-axis complements the x-axis by providing vertical positioning. Imagine a vertical line that intersects the x-axis at the origin (0,0) and runs up and down the paper. Here's how it works:
  • Positive y-values are above the origin. A value like +2 tells you to move 2 units up from the horizontal line.
  • Negative y-values are below the origin. For point M, with a y-coordinate of -3, you would move 3 units down from wherever you are along the x-axis.
When combined with the movement from the x-axis, the y-axis allows you to pinpoint the exact vertical location of a point. By plotting these two movements together, the precise location \((-4, -3)\) is marked on the graph, symbolizing point M.

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Most popular questions from this chapter

Solve each proportion. \(\frac{x}{3}=\frac{12}{18}\)

\(\frac{?}{N H}=\frac{G M}{M I}\)

Determine whether each statement is always, sometimes, or never true. Similar polygons are also congruent.

\(\frac{?}{\mathrm{MN}}=\frac{G H}{G N}\)

Short Response \(\operatorname{In} \triangle A C E, \overline{A C} \cong \overline{A E}\). If \(m \angle C=7 x+2\), and \(m \angle E=8 x-8\), what is \(m \angle C\) and \(m \angle E\) ? (Lesson \(6-4\) )
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