Question

On paper, make a rectangle that has points A and B as two of its vertices and has a perimeter of 40 units. Draw and label the two other vertices as points C and D on the coordinate plane. Draw line segments to show the rectangle. What are the coordinates for points C and D.

Answer 1

Answer:

$A(x,y),B(x+10,y),C(x+10,y-10) \:and\: D(x,y-10)$

Step-by-step explanation:

If a Rectangle has a perimeter of 40 units, then we can write that formula and find the a formula for the coordinates:

$\left\{\begin{matrix}w+l=20 & \\ w*l=100 & \end{matrix}\right.\Rightarrow w=20-l\Rightarrow (20-l)l=100\Rightarrow -l^2+20l-100=0\Rightarrow l^2-20l+100\Rightarrow (l-10)(l-10)\Rightarrow l=10\therefore l=10\: and\: w=10$

Therefore we can say:

$A(x,y),B(x+10,y),C(x+10,y-10) \:and\: D(x,y-10)$

Technically when $w=l$in this rectangle is a square, a degenerate square.