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    Mathematics
    Grade9
    Easy

    Question

    The vertices of triangleABC are A(2, 1), B(4, 3), and C(6, 1). Use scalar multiplication to find the image of triangleABC after a dilation with its center at the origin and a scale factor of 2. Find the coordinates of the image.

    1. open square brackets table row 4 8 12 row 2 6 2 end table close square brackets
    2. open square brackets table row 8 8 12 row 2 6 2 end table close square brackets
    3. open square brackets table row 4 8 12 row 4 6 2 end table close square brackets
    4. open square brackets table attributes columnalign left end attributes row 4 8 12 row 2 6 12 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 4 8 12 row 2 6 2 end table close square brackets

      G i v e n comma F o r space increment A B C comma A open parentheses x subscript 1 comma y subscript 1 close parentheses space equals space A open parentheses 2 comma 1 close parentheses B open parentheses x subscript 2 comma y subscript 2 close parentheses space equals space B open parentheses 4 comma 3 close parentheses C open parentheses x subscript 3 comma y subscript 3 close parentheses space equals space C open parentheses 6 comma 1 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 A apostrophe open parentheses x subscript 4 comma y subscript 4 close parentheses B apostrophe open parentheses x subscript 5 comma y subscript 5 close parentheses C 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 2 open square brackets table attributes columnalign left end attributes row 2 4 6 row 1 3 1 end table close square brackets equals open square brackets table row 4 8 12 row 2 6 2 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 A B C space a r e open square brackets table row 4 8 12 row 2 6 2 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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