A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair 4, 1, vertex B on ordered pair 3, 1, and vertex C on ordered pair 4, 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 4, 4, vertex B prime on ordered pair negative 3, 4, and vertex C prime on ordered pair negative 3, 1. What set of transformations is performed on triangle ABC to form triangle A'B'C'?

Check the picture.

since the choices all have rotation about the origin, we must shift the original triangle in a suitable position. This is done by connecting any of the points of A'B'C' to the origin, and extend this line segment, as shown in the picture.

The most appropriate point is C', and we draw C" such that C'O=OC", and C', O and C" are collinear.

We see that the distance CC'' is 5.

So

Answer is:

"A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin"

Step-by-step explanation:

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.