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Dilate triangle ABC by a factor of 2 around point A. What are the coordinates of B Q1 (1,0) Q2 (1,-1) Q3 (1,-2) Q4 (2,-4)

Dilate triangle ABC by a factor of 2 around point A. What are the coordinates of B-example-1
User Eerorika
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2 Answers

3 votes
The answer would be Q3 (1,-2)
User Gopherine
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8.1k points
5 votes

Answer:

Option 3: (1,-2)

Explanation:

From the given figure it is clear that the vertices of triangle ABC are A(1,4), B(1,1), C(4,1).

If a figure dilated by the factor k and the center of dilation is point (a,b), then the rule of dilation is


(x,y)\rightarrow (k(x-a)+a,k(y-b)+b)

The figure ABC dilated by the factor 2 and the center of dilation is point A(1,4).


(x,y)\rightarrow (2(x-1)+1,2(y-4)+4)


(x,y)\rightarrow (2x-2+1,2y-8+4)


(x,y)\rightarrow (2x-1,2y-4)

The coordinates of B after dilation are


B(1,1)\rightarrow B'(2(1)-1,2(1)-4)


B(1,1)\rightarrow B'(1,-2)

The coordinates of B after dilation are (1,-2).

Therefore, the correct option is 3.

User Ateev Chopra
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