Question

Question 5 Perform any sequence of three rigid transformations on AABC to change its position. (Be sure to form a polygon with points A, B, and Cas vertices before performing the transformations on the triangle. Also, consider turning on the grid.) Record the sequence of transformations that you used. Then calculate the area of the transformed triangle. How is the area of the image of ABC related to the area of ABC?

Answer 1

The sequence of transformations will vary. The answer provided here is based on this sequence: a reflection across the x-axis, a translation 4 units up, and a 45° counterclockwise rotation about the origin.

base of A'B'C" = 5 units

height of A'BC" = 12 units

area of A'B'C" = 1/2 (base) (height) = 1/2 (5 units) (12 units) = 30 units^2

The area of A'B'C" is the same as that of ABC.

Explanation:

plato

Answer 2

We have the following:

The transformations are as follows:

0. 270 ° rotation clockwise

,

1. Translation of -8 units on the y-axis

,

2. Translation of +20 units on the x-axis

We calculate the area of a triangle knowing that the area is equal to

`A=(b\cdot h)/(2)`

replacing

b = 15 and h = 4

`\begin{gathered} A=(15\cdot4)/(2) \\ A=(60)/(2) \\ A=30 \end{gathered}`

The area is 30 square units

now, since the figure did not have any change in the length of the sides, the area is equal to both the original triangle and the image

0.