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Chapter 11: Problem 4

Plot each point on a coordinate grid. \((3,4)\)

Short Answer

Expert verified
Plot at 3 units to the right and 4 units up from the origin.

Step by step solution

01

Understand the Coordinate System

A coordinate grid is composed of an x-axis (horizontal line) and a y-axis (vertical line). Points on this grid are represented as \((x, y)\).
02

Identify the Coordinates

The given point is \((3,4)\). Here, 3 is the x-coordinate (horizontal position), and 4 is the y-coordinate (vertical position).
03

Locate the x-coordinate

Start from the origin (0,0) of the coordinate grid. Move 3 units to the right along the x-axis.
04

Locate the y-coordinate

From the position of the x-coordinate, move 4 units upwards along the y-axis.
05

Plot the Point

Mark the point where these two movements intersect. This is the location of the point \((3,4)\).

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Key Concepts

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

Coordinate System
A coordinate system helps us locate points in space.
It's like a map.
This map has two main lines: the x-axis and the y-axis.
They cross each other at the origin.
These two axes divide the space into four parts called quadrants.

Imagine you're standing at the origin.
You can move left or right along the x-axis and up or down along the y-axis.
Any point on this grid can be represented by an ordered pair \((x, y)\), where \x\ is the horizontal position and \y\ the vertical.
x-axis
The x-axis is a horizontal line in the coordinate system.
It's like the ground you walk on.
All positions to the right of the origin are positive numbers.
All positions to the left are negative numbers.

If you want to locate a point such as (3, 4), you first move along the x-axis.
Start from the origin (0,0).
Move 3 units to the right.
The x-coordinate tells us how far left or right to go.
y-axis
The y-axis is a vertical line.
Think of it as a ladder.
All positions above the origin are positive numbers and all below are negative.

Using our point (3, 4), we have already moved 3 units to the right along the x-axis.
Next, you need to move upwards along the y-axis.
Move 4 units up.
This will help you place our point correctly on the coordinate grid.
Origin
The origin is the starting point of our coordinate grid.
It is represented as (0,0).
It's where the x-axis and y-axis intersect.
Think of it as your home base.

From the origin, you can move both horizontally along the x-axis and vertically along the y-axis.
To plot the point (3, 4), we start at the origin, move right 3 units, then up 4 units.
The intersection point is where our point lies on the grid.

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