Question

A. 2C. 3T72T? 1♥32N34F 5In the similaritytransformation of AABCto AEDF, AABC was dilated bya scale factor of [?], reflectedacross the [ ], and movedthrough the translation [ 1.B. 1/2D. 1/3

Answer 1

Triangle ABC was dilated by a factor of 1/2, reflected across the y-axis, and moved through the translation 2 units up and 3 units right

Step-by-step explanation

We can see that triangle ABC is greater than triangle EDF, so the scale factor will be a number slower than 1. To find the scale factor, we will use the length of AB = 4 units and the length of DE = 2 units. Then

DE/AB = 2/4 = 1/2

So, the scale factor is 1/2.

With this transformation, the new coordinates of ABC will be

A(-4, -2) ----> 1/2(-4, -2) = A'(-2, -1)

B(0, -2) ----> 1/2(0, -2) = B'(0, -1)

C(-2, -4)----> 1/2(-2, -4) = C'(-1, -2)

Now, we need to reflect the figure across the y-axis. Because this will result in the same figure but on the right side of the y-axis. Therefore, the reflection is across the y-axis.

After the reflection, the coordinates will be

(x, y) ----------> (-x, y)

A'(-2, -1) -----> A''(2, -1)

B'(0, -1) -----> B''(0, -1)

C'(-1, -2) -----> C''(1, -2)

Finally, we need to translate the figure 2 units up and 3 units to the right, so we will use the translation

(x, y) ------> (x + 3, y + 2)

A''(2, -1) ---> (2 + 3, -1 + 2) = E(5, 1)

B''(0, -1) ---> (0 + 3, -1 + 2) = D(3, 1)

C''(1, -2) ---> (1 + 3, -2 + 2) = F(4, 0)

So, the translation is 2 units up and 3 units right.