 How to Create a Figure for an Analytic Proof - dummies

When you do an analytic proof, your first step is to draw a figure in the coordinate system and label its vertices. This figure will make the algebra part easier, when you have to prove something about the figure.

Here’s an example. Say you’re given the following proof: First, prove analytically that the midpoint of the hypotenuse of a right triangle is equidistant from the triangle’s three vertices, and then show analytically that the median to this midpoint divides the triangle into two triangles of equal area.

Your first step in an analytic proof is to draw a figure in the x-y coordinate system and give its vertices coordinates. You want to put the figure in a convenient position that makes the math work out easily. For example, sometimes putting one of the vertices of your figure at the origin, (0, 0), makes the math easy because adding and subtracting with zeros is so simple. Quadrant I is also a good choice because all coordinates are positive there.