A vector could be represented by an ordered pair (x,y) but it
could also be represented by a column matrix:
Polygons could also be represented in matrix form, we simply
place all of the coordinates of the vertices into one matrix. This
is called a vertex matrix.
A square has its vertexes in the following coordinates (1,1),
(-1,1), (-1,-1) and (1,-1). If we want to create our vertex matrix
we plug each ordered pair into each column of a 4 column
We can use matrices to translate our figure, if we want to
translate the figure x+3 and y+2 we simply add 3 to each
x-coordinate and 2 to each y-coordinate.
If we want to dilate a figure we simply multiply each x- and
y-coordinate with the scale factor we want to dilate with.
When we want to create a reflection image we multiply the vertex
matrix of our figure with what is called a reflection matrix. The
most common reflection matrices are:
for a reflection in the x-axis
for a reflection in the y-axis
for a reflection in the origin
for a reflection in the line y=x
We want to create a reflection of the vector in the x-axis.
In order to create our reflection we must multiply it with
correct reflection matrix
Hence the vertex matrix of our reflection is
If we want to rotate a figure we operate similar to when we
create a reflection. If we want to counterclockwise rotate a figure
90° we multiply the vertex matrix with
If we want to counterclockwise rotate a figure 180° we multiply
the vertex matrix with
If we want to counterclockwise rotate a figure 270°, or
clockwise rotate a figure 90°, we multiply the vertex matrix
Video lesson: Rotate the vector A 90° counter
clockwise and draw both vectors in the coordinate plane