Question

A rectangle with length three times its width needs to be placed on the coordinate plane for use in a coordinate proof.

(a) Describe how to place the rectangle on the coordinate plane.
(b) Tell what the coordinates of the vertices would be. Use variables for nonzero coordinates.

Answer 1

We have a rectangle with two sides a and b, with length three times its width. So let's name:

a = length
b = width

So, according to the relation:


`a=3b`

Part a)

First of all we draw the rectangle as shown in the figure 1. To place this rectangle on the coordinate plane we will take a point (x, y) and name it v1 that is the vertex 1. Next we will name the other vertices as v2, v3 adn v4. Finally, the segment v1v2 must be parallel to the x-axis

Part b)

Given that the vertex v1(x, y). As shown in the figure 2, v2 has the same value of y, but x increases 3b, so v2(x+3b, y). Applying the same reasoning to v3 and v4, we hava:

v1(x, y)
v2(x+3b, y)
v3(x, y+b)
v4(x+3b, y+b)