Question

1. triangle abc is similar to triangle def. triangle abc has vertices a(2, 2), b(4, 2) and c(4, 6). triangle def has vertices d(3, - 3), e(6, - 3) and f(6, - 9). write a sequence of transformations to map △abc onto △def to prove similarity.

Explanation:

Step1: Analyze horizontal translation

First, look at the x - coordinates of corresponding vertices. For point A(2, 2) and D(3, - 3), to get from the x - coordinate of A to the x - coordinate of D, we need to add 1. For point B(4, 2) and E(6, - 3), and point C(4, 6) and F(6, - 9), the same horizontal translation of adding 1 to the x - coordinate occurs.

Step2: Analyze vertical translation

Looking at the y - coordinates of corresponding vertices. For point A(2, 2) and D(3, - 3), we need to subtract 5 from the y - coordinate of A to get the y - coordinate of D. For B(4, 2) and E(6, - 3), and C(4, 6) and F(6, - 9), the same vertical translation of subtracting 5 from the y - coordinate occurs.

Step3: Determine the sequence of transformations

The sequence of transformations is a translation 1 unit to the right and 5 units down.

Answer:

Translate △ABC 1 unit to the right and 5 units down to map it onto △DEF.