Polygon abcde is the first in a pattern for a high school art project. the polygon is transformed so that the image of a' is at (−4, 2) and the image of d' is at (−2, 1). which transformation can be used to show that abcde and its image are congruent?
a. rotate abcde 90° counterclockwise.
b. translate abcde left 4 units and down 2 units.
c. reflect abcde over the y-axis.
d. rotate abcde 90° clockwise.

ANSWER

A. Rotate ABCDE 90° counterclockwise.

EXPLANATION

When we rotate a point through 90° counterclockwise, the mapping is

The coordinates of A are (2,4) and the coordinates of A' are (-4,2)

The coordinates of D are (1,2) and the coordinates of D' are (-2,1).

We can observe that the x and y coordinates swapped position and the first coordinate was then negated.

This is a 90° counterclockwise rotation about the origin.

Since rotation is a rigid motion the two shapes are congruent.

The correct answer is

A. Rotate ABCDE 90° counterclockwise.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!