Word Problems: Plotting Points

Now that you've studied the Cartesian plane and understand how to plot points, you might be thinking that it's time to move on to a new topic. Not so fast! In this article, we'll explore word problems involving points on the Cartesian plane. Let's begin.

Working out word problems: plotting points

Word problems involving the Cartesian plane are usually dense with information, so it's important to read them carefully.

For example, the city of Vanda is laid out in a square grid with square city blocks. Joseph started on the intersection between Idly Street and Puttu Avenue, walking 4 blocks north and then 5 blocks west. His friend Nisha started at the same intersection but walked 6 blocks south, then 2 blocks east, then 10 blocks north. Assuming $\left(0,0\right)$ is the origin point, what coordinates represent Joseph's location and how far away is he from Nisha?

Solving this in our heads would be borderline impossible, so let's plot these points on the Cartesian plane so we have a visual aid. Based on the information above, our graph should look something like this:

Joseph's coordinates are $\left(5,4\right)$ , meaning we've already solved the first part of the problem. To figure out how far Joseph is from Nisha, we'll need her coordinates as well $\left(2,4\right)$ . Both Joseph and Nisha have the same y-coordinates, which means the distance between them is the absolute value of the difference between their x-coordinates.

$|\left(2\right)-\left(-5\right)|=7$

Joseph is 7 units away from Nisha. We're finished!

Plotting points: try it yourself

The following Cartesian plane illustrates how far certain places are from Mick's home:

a. What is the distance between his home and the sports complex?

b. How far is his home from the swimming pool?

c. How far is the school from the dance academy?

Problems like these become easier if you know the specific coordinates of each location, so let's add that information to our illustration:

Now that we have coordinates, things should be much more manageable. The sports complex and Mick's home share the same x-coordinates, meaning the distance between them is the absolute value of the distance between their y-coordinates:

$\left|-4-3\right|=7\mathrm{units}$

Similarly, Mick's home and the swimming pool share y-coordinates, meaning the distance between them is the absolute value of the difference between their x-coordinates:

$\left|2-\left(-2\right)\right|=4\mathrm{units}$

Finally, the school and dance academy share the same y-coordinates, which means the absolute value of the difference between their x-coordinates will give us our answer:

$\left|1-\left(-5\right)\right|=6\mathrm{units}$

We've answered all of the questions. Note that we have coordinates for the market but were never asked to use them. It's important to ignore extra information and concentrate on what you need to solve the problem in front of you.

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