Question

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)

Answer 1

The answer would be Q3 (1,-2)

Answer 2

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.