Each column of the matrix cap A is equal to the 2 by 4 matrix, row 1, column 1, 1 column 2, 6 column 3, 6 column 4, 1 row 2, column 1, 1 column 2, 1 column 3, 5 column 4, 5 represents a vertex of a rectangle on the coordinate plane. If Fan scales the rectangle by finding 4 cap A , what are the vertices of the scaled rectangle?
Answer
A
open paren 5 comma 5 close paren comma open paren 10 comma 5 close paren comma open paren 10 comma 9 close paren comma open paren 5 comma 9 close paren
B
open paren 5 comma 5 close paren comma open paren 6 comma 1 close paren comma open paren 6 comma 5 close paren comma open paren 4 comma 20 close paren
C
open paren 4 comma 4 close paren comma open paren 6 comma 1 close paren comma open paren 6 comma 5 close paren comma open paren 1 comma 5 close paren
D
open paren 4 comma 4 close paren comma open paren 24 comma 4 close paren comma open paren 24 comma 20 close paren comma open paren 4 comma 20 close paren
Explanation
The columns of A give the rectangle’s vertices: (1, 1), (6, 1), (6, 5), and (1, 5). Multiplying A by 4 multiplies each coordinate by 4, so the scaled vertices are (4, 4), (24, 4), (24, 20), and (4, 20). These are the vertices listed in choice C.
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