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Chapter 1: Problem 16

Sketch a set of coordinate axes and then plot the point. $$ (3,-4) $$

Short Answer

Expert verified
To plot the point (3, -4) on the coordinate axes, first draw the axes and label them as x-axis and y-axis. Locate the origin (0,0) and move 3 units to the right along the x-axis, and then 4 units downwards along the y-axis. Mark and label the point (3, -4). Check your work by verifying that the point is in the correct position relative to the origin.

Step by step solution

01

Draw coordinate axes

Begin by drawing a set of coordinate axes on a piece of paper or a whiteboard. It might be helpful to add arrowheads to the ends of these lines to indicate that they go on infinitely.
02

Label the axes and identify the origin

Label the horizontal axis as the x-axis and the vertical axis as the y-axis. Mark the point where these two lines intersect and label it as the origin (0,0).
03

Locate the x-coordinate of the point

From the origin (0,0), move 3 units to the right along the x-axis. Remember that moving to the right on the x-axis increases the x-coordinate, while moving to the left decreases it. Since our x-coordinate is positive, we move to the right.
04

Locate the y-coordinate of the point

From the point found in step 3, move 4 units vertically downwards. Remember that moving upwards on the y-axis increases the y-coordinate, while moving downwards decreases it. Since our y-coordinate is negative, we move downwards.
05

Plot the point and label it

Mark the point where we ended up after completing steps 3 and 4 and label it with the given coordinates (3, -4). This point represents the location of the coordinates (3, -4) in the Cartesian coordinate system.
06

Double-check your work

Verify that your point is plotted correctly on the coordinate axes by checking the x and y-coordinates. The point should be 3 units to the right of the origin along the x-axis and 4 units below the origin along the y-axis.

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