Question

The endpoints of AB are A(3,2) and B(7,1). If A"B" is the result of the transformation of AB under the sequence T(-4,3) followed by a dilation of 2 about the origin, what are the coordinates of A" and B"?

a) A"(-2,6) and B"(-6,3)

b) A"(-10,0) and B"(-14,-1)

c) A"(-8,8) and B"(-12,4)

d) A"(6,3) and B"(14,2)

Answer 1

After transforming segment AB with endpoints A(3,2) and B(7,1) by applying the translation T(-4,3) followed by a dilation of 2, we should obtain the points A"(-2,10) and B"(6,8). However, these coordinates do not match any of the options provided.

Step-by-step explanation:

The transformation of segment AB with endpoints A(3,2) and B(7,1) under the sequence T(-4,3) followed by a dilation of 2 about the origin involves two steps. First, we apply the translation T(-4,3) to each endpoint, resulting in A' and B'. To find A', we add the translation vector to A: A' = (3-4, 2+3) = (-1,5). For B', we do the same with point B: B' = (7-4, 1+3) = (3,4).

Next, we apply the dilation of 2 about the origin to A' and B'. This can be done by multiplying each coordinate of A' and B' by the scale factor 2. Therefore, A" = (-1*2, 5*2) = (-2,10) and B" = (3*2, 4*2) = (6,8).

However, none of the given answer options match these resulting coordinates, so it is possible that there is an error in the question or the provided answer choices.