What is the coodinates of a rectangle?

Answer 1

Let's place the rectangle with one corner at the origin. Then one coordinate is (0,0) call this the lower left corner. Now the lower right corner must have a y coordinate of 0 and we call the x the coordinate L for the length of the rectangle. So the lower right corner is (L,0)
Now the upper left corner is (0,H) where H is the height of the rectangle.
The last corner is the upper right and it (L, H).


So the coordinates are (0,0), (L,0), (0,H), (L,H) where L is the length and H is the height.
Now we can move or translate the rectangle anywhere we want on the plane.


For example, let's move the lower left corner horizontally by 3


Then the new x coordinate of the lower left side is 3 so it at (3,0) The lower right side is (L+3,0), the upper right side is (L+3,H) and the upper left side is (3, H)


Perhaps you now want to move the rectangle up vertically, say 4. (We already moved it horizontally 3 so we leave that.) So the new y value for the lower left coordinate is 4
The left lower corner is at (3, 4)
The lower right corner is (L+3, 4)
The upper left corner is (3, H+4) and
the upper right corner is (L+3, H+4)




What we just did is known as a rigid motion.

Any way of moving all the points in the plane such that

a) the relative distance between points stays the same and

b) the relative position of the points stays the same

is called a rigid motion.

More specifically, it is a translation,
In Euclidean geometry a transformation in which the origin of a coordinate system is moved to another position but the new axes are parallel to the old; a change of variables of the form
x' = x + a, y' = y + b. In our case a=3 and b=4
We can either think of moving the rectangle, OR we can look it as leaving the rectangle where it is and moving the coordinate system.