2.1 The Coordinate Plane

We first introduce the coordinate plane.

Then we used the distance formula d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} as well as the midpoint formula M = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) to find the distance and midpoint between two points.

If you need extra distance and midpoint problems, here is a worksheet.

Then we graphed some equations by plotting points.

In particular when graphing, we’re interested in any “interesting” points, for example, when the graph intersects with either the x-axis or y-axis. To do this, we set y=0 and x=0 respectively, and solve for the other variable.

Circles

We then derived the equation of a circle with center (h,k) and radius r.

    \[(x-h)^2+(y-k)^2=r^2\]

We can use this to create equations of circles.

Sometimes we’re given the equation of a circle not in standard form, so we have to put it in that form by completing the square. Twice.

Here are some practice problems for circles.