To find the image of a triangle for a dilation centered at the origin, multiply each element in the vertex matrix for the triangle by the scale factor. Multiplying a matrix by a number in this way, as with vectors, is called scalar multiplication.

Example 3

Δ A B C cap delta eh b c  has vertices A ( − 2 , 2 ) , B ( 1 , − 1 ) ,  and  C ( 2 , 1 1 2 ) . eh . open , negative 2 comma 2 , close . comma b . open , 1 comma negative 1 , close . comma , and c . open . 2 comma 1 , and 1 half . close . .  Use scalar multiplication to find the image of Δ A B C cap delta eh b c  for a dilation with center (0, 0) and scale factor 2. Graph Δ A B C cap delta eh b c  and its enlargement.

x - coordinate y - coordinate A B C [ − 2 1 2 2 − 1 1 1 2 ] Write a matrix for  Δ A B C .   2 · [ − 2 1 2 2 − 1 1 1 2 ] = [ − 4 2 4 4 − 2 3 ] Multiply each element of the matrix by the scale factor  2 . table with 2 rows and 3 columns , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , x minus . coordinate , row2 column 1 , y minus . coordinate , end table , column 2 table with 2 rows and 1 column , row1 column 1 , eh b c , row2 column 1 , . matrix with 2 rows and 3 columns , row1 column 1 , negative 2 , column 2 1 , column 3 2 , row2 column 1 , 2 , column 2 negative 1 , column 3 1 , and 1 half , end matrix , end table , column 3 cap writeamatrixfor . cap delta eh b c . , row2 column 1 , , column 2 2 middle dot . matrix with 2 rows and 3 columns , row1 column 1 , negative 2 , column 2 1 , column 3 2 , row2 column 1 , 2 , column 2 negative 1 , column 3 1 , and 1 half , end matrix , column 3 equals . matrix with 2 rows and 3 columns , row1 column 1 , negative 4 , column 2 2 , column 3 4 , row2 column 1 , 4 , column 2 negative 2 , column 3 3 , end matrix . table with 2 rows and 1 column , row1 column 1 , cap multiplyeachelementofthe , row2 column 1 , matrixbythescalefactor . 2 . , end table , end table

The vertices of the enlargement are A ′ ( − 4 , 4 ) , B ′ ( 2 , − 2 ) , and  C ′ ( 4 , 3 ) . eh prime , open negative 4 comma 4 close comma , b prime , open 2 comma negative 2 close comma , and , c prime , open 4 comma 3 close .