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Question 9 (1 point)
Transformations by Scale Factors

The vertices of triangle [tex]$ABC$[/tex] are [tex]$A(2,2), B(4,2),$[/tex] and [tex]$C(4,3)$[/tex].
If the given triangle is dilated by a factor of 2, what are the coordinates of [tex]$A'B'C'$[/tex]?

A. [tex]$\quad A'(0,0), B'(2,0), C'(3,1)$[/tex]

B. [tex]$\quad A'(4,4), B'(8,4), C'(8,6)$[/tex]

C. [tex]$\quad A'(4,4), B'(6,4), C'(6,5)$[/tex]

D. [tex]$\quad A'(1,1), B'(2,1), C'\left(2, \frac{3}{2}\right)$[/tex]



Answer :

GinnyAnswer
To find the coordinates of the new triangle [tex]\( A'B'C' \)[/tex] after dilation, we need to apply the given scale factor to each vertex of the original triangle [tex]\( ABC \)[/tex].

The vertices of triangle [tex]\( ABC \)[/tex] are:
- [tex]\( A(2, 2) \)[/tex]
- [tex]\( B(4, 2) \)[/tex]
- [tex]\( C(4, 3) \)[/tex]

The dilation factor is 2, so we multiply each coordinate by 2:

1. For [tex]\( A \)[/tex]:
[tex]\[ A' = (2 \cdot 2, 2 \cdot 2) = (4, 4) \][/tex]

2. For [tex]\( B \)[/tex]:
[tex]\[ B' = (4 \cdot 2, 2 \cdot 2) = (8, 4) \][/tex]

3. For [tex]\( C \)[/tex]:
[tex]\[ C' = (4 \cdot 2, 3 \cdot 2) = (8, 6) \][/tex]

So, the coordinates of [tex]\( A', B', \)[/tex] and [tex]\( C' \)[/tex] after dilation are:
- [tex]\( A'(4, 4) \)[/tex]
- [tex]\( B'(8, 4) \)[/tex]
- [tex]\( C'(8, 6) \)[/tex]

Given the multiple choice options, the correct answer is:

B [tex]\( \quad A^{\prime}(4,4), B^{\prime}(8,4), C^{\prime}(8,6) \)[/tex]