Mathematics
Grade9
Easy

Question

The vertices of triangleLMN are L(-3, 6), M(0, 3), and N(-6, 0). Use scalar multiplication to find the image of triangleLMN after a dilation with its center at the origin and a scale factor of  1 third. Find the coordinates of the image.

  1. open square brackets table row 1 0 cell negative 2 end cell row 2 1 0 end table close square brackets
  2. open square brackets table row cell negative 1 end cell 0 2 row 2 1 0 end table close square brackets
  3. open square brackets table row cell negative 1 end cell 0 cell negative 2 end cell row cell negative 2 end cell 1 0 end table close square brackets
  4. open square brackets table row cell negative 1 end cell 0 cell negative 2 end cell row 2 1 0 end table close square brackets

hintHint:

Find out the co-ordinates of the image of the triangle by the multiplication of scale factor with matrix of the coordinates of the given triangle.

The correct answer is: open square brackets table row cell negative 1 end cell 0 cell negative 2 end cell row 2 1 0 end table close square brackets


    G i v e n comma
F o r space increment L M N comma
L open parentheses x subscript 1 comma y subscript 1 close parentheses space equals space L open parentheses negative 3 comma 6 close parentheses
M open parentheses x subscript 2 comma y subscript 2 close parentheses space equals space M open parentheses 0 comma 3 close parentheses
N open parentheses x subscript 3 comma y subscript 3 close parentheses space equals space N open parentheses negative 6 comma 0 close parentheses
S c a l e space f a c t o r space equals space 2

T o space f i n d comma
L apostrophe open parentheses x subscript 4 comma y subscript 4 close parentheses
M apostrophe open parentheses x subscript 5 comma y subscript 5 close parentheses
N apostrophe open parentheses x subscript 6 comma y subscript 6 close parentheses
H e r e comma
W e space w i l l space u s e space s c a l a r space m u l t i p l i c a t i o n space t o space f i n d space t h e space c o o r d i n a t e s space o f space t h e space i m a g e.

T h e r e f o r e comma
open parentheses S c a l e space f a c t o r close parentheses open square brackets table attributes columnalign left left left end attributes row cell x subscript 1 end cell cell x subscript 2 end cell cell x subscript 3 end cell row cell y subscript 1 end cell cell y subscript 2 end cell cell y subscript 3 end cell end table close square brackets equals open square brackets table attributes columnalign left left left end attributes row cell x subscript 4 end cell cell x subscript 5 end cell cell x subscript 6 end cell row cell y subscript 4 end cell cell y subscript 5 end cell cell y subscript 6 end cell end table close square brackets
1 third open square brackets table row cell negative 3 end cell 0 cell negative 6 end cell row 6 3 0 end table close square brackets equals open square brackets table row cell negative 1 end cell 0 cell negative 2 end cell row 2 1 0 end table close square brackets

T h e r e f o r e comma space t h e space c o o r d i n a t e s space o f space t h e space i m a g e space o f space increment L M N space a r e
open square brackets table row cell negative 1 end cell 0 cell negative 2 end cell row 2 1 0 end table close square brackets

    Dilation is a process of changing the size of an object or shape by decreasing or increasing its dimensions by some scaling factors.

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