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Mathematics

Grade9

Easy

Question

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

$[\begin{matrix} 4 & 8 & 12 \\ 2 & 6 & 2 \end{matrix}]$
$[\begin{matrix} 8 & 8 & 12 \\ 2 & 6 & 2 \end{matrix}]$
$[\begin{matrix} 4 & 8 & 12 \\ 4 & 6 & 2 \end{matrix}]$
$[\begin{array}{l} 4 & 8 & 12 \\ 2 & 6 & 12 \end{array}]$

hint Hint:

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.

Related Questions to study

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Find the value of m.

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$negative 3 open square brackets table row cell negative 4 end cell 1 0 row 9 cell negative 5 end cell cell negative 7 end cell end table close square brackets$

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Simplify the product.
$4 open square brackets table row 2 1 cell negative 10 end cell row 3 cell negative 4 end cell 7 end table close square brackets$

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Find the scale factor.

Find the scale factor.

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Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement.

If the scale factor is more than 1, then the image stretches.
If the scale factor is between 0 and 1, then the image shrinks.
If the scale factor is 1, then the original image and the image produced are congruent.

Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement.

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If the scale factor is more than 1, then the image stretches.
If the scale factor is between 0 and 1, then the image shrinks.
If the scale factor is 1, then the original image and the image produced are congruent.

Find the scale factor, given $stack A B with bar on top space$ = 15m and $stack A apostrophe B apostrophe with bar on top space equals 10 m$ .

Find the scale factor, given $stack A B with bar on top space$ = 15m and $stack A apostrophe B apostrophe with bar on top space equals 10 m$ .

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Find the scale factor, given $stack C D with bar on top space$ = 5m and $stack C apostrophe D apostrophe with bar on top space equals 10 m$ .

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Given the scale factor is 2.5, state the dilation.

If the scale factor is more than 1, then the image stretches.
If the scale factor is between 0 and 1, then the image shrinks.
If the scale factor is 1, then the original image and the image produced are congruent

Given the scale factor is 2.5, state the dilation.

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If the scale factor is more than 1, then the image stretches.
If the scale factor is between 0 and 1, then the image shrinks.
If the scale factor is 1, then the original image and the image produced are congruent

parallel

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