How to Draw in a Coordinate System

In this section, you’ll learn how to draw geometric figures in a coordinate system. That means you’ll be able to draw triangles, squares, and circles using coordinates and distances. A coordinate is a point in a coordinate system. It’s made up of one value from the $x$ -axis and one value from the $y$ -axis and looks like this: $(x, y)$ . When you draw geometric figures in a coordinate system, you make crosses or dots at given coordinates, then draw lines between them. A typical assignment might be to have you find a final coordinate based on some given coordinates and a description of the figure.

Example 1

Given the points $(0, 0)$ and $(4, 2)$ , where do you have to put the final point to make a right triangle?

In this case there are two points that satisfy the demand for a right triangle. If you move along the $x$ -axis to $x = 4$ , you can turn $90$ ° and move directly to the point $(4, 2)$ . That means you can choose the point $(4, 0)$ to make a right triangle. If you move along the $y$ -axis to $y = 2$ , you can turn $90$ ° to the right and move straight to the point $(4, 2)$ . That means you can choose the point $(0, 2)$ to make a right triangle as well.

Example of right triangles in a coordinate system

Example 2

Draw a circle with its center at $(- 2, - 4)$ and a radius of 3

In this case you first mark the center on the graph. Then, set up your draft compass with distance 3 between the legs. Put the point of the compass in the center and make a circle.

Example of a circle in a coordinate system

Example 3

You’re going to draw a square. You know that two of the corners are at $(- 3, - 2)$ and $(2, 3)$ . Find the rest of the coordinates and draw the square.

There are multiple solutions to this problem, but you decide you will consider only the square with sides parallel to the $x$ - and $y$ -axes.

First, mark the points you already know: $(- 3, - 2)$ and $(2, 3)$ . Then you find the distance between the $x$ values ( $2 - (- 3) = 2 + 3 = 5$ ) and the distance between the $y$ values ( $3 - (- 2) = 3 + 2 = 5$ ). Choose one of the given points. Move 5 in the $x$ direction towards the other point. Mark a point. Next, move 5 in the $y$ direction from your chosen point towards the other point and mark that point. Those are the final points of the square.

Example of a square in a coordinate system

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What Are Loci in Geometry?

What Are Tangent Lines?

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