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Chapter 1: Problem 14

Sketch a set of coordinate axes and then plot the point. $$ (1,3) $$

Short Answer

Expert verified
Draw a horizontal x-axis and a vertical y-axis, intersecting at the origin (0,0). Mark the units, 1 unit for each integer value. Move 1 unit to the right from the origin along the x-axis and 3 units up along the y-axis. Plot the point, mark it with a dot, and label it (1,3). Verify the position by ensuring the point is horizontally aligned with (1,0) and vertically aligned with (0,3).

Step by step solution

01

1. Prepare the coordinate axes

First, draw a horizontal line, called the x-axis, and a vertical line, called the y-axis, intersecting at a point called the origin (0,0). These two lines will represent our Cartesian plane. Make sure to label the x-axis and y-axis.
02

2. Mark the units on the axes

Choose an appropriate scale, and mark the units along the x-axis (horizontal) and y-axis (vertical). In this case, the scale can be set 1 unit for each integer value as we are given the point (1,3). These axes will represent the position of the point in the Cartesian plane.
03

3. Locate the point on the axes

The point in our exercise is given as (1,3). On a Cartesian plane, the first value of a point (x-coordinate) represents the horizontal position on the x-axis and the second value of a point (y-coordinate) represents the vertical position on the y-axis. Since the x-coordinate of our point is 1, move 1 unit to the right from the origin along the x-axis. Similarly, since the y-coordinate of our point is 3, move 3 units up from the origin along the y-axis.
04

4. Plot the point

Now that we have moved 1 unit right on the x-axis and 3 units up on the y-axis, plot the point at this position by marking it with a dot. After plotting the point, label it with the given coordinates (1,3) to avoid confusion.
05

5. Verify the position

Finally, verify if the plotted point is in the correct position in the Cartesian plane by checking its x and y coordinates. The point should be horizontally aligned with point (1,0) and vertically aligned with point (0,3). If the plotted point is aligned with both of these points, the point (1,3) has been accurately represented on the Cartesian plane.

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