Which sequence of transformations produces TriangleL'M'N' from TriangleLMN? a translation 5 units down and 2 units to the right followed by a reflection across the y-axis a reflection across the y-axis followed by a translation 5 units down and 2 units right a translation 5 units down and 2 units to the left followed by a reflection across the y-axis no sequence of transformations

A translation 5 units down and 2 units to the right followed by a reflection across the y-axis

Step-by-step explanation:

The rest of the questions is the attached figure.

The coordinates of Δ LMN ⇒ L(2,1) , M(1,1) , N(1,3)

The coordinates of Δ L'M'N' ⇒ L'(-4,-4) , M'(-3,-4) , N'(-3,-2)

So, the reasonable transformations will be:

A translation 5 units down and 2 units to the right followed by a reflection across the y-axis

The rule of a translation 5 units down and 2 units to the right

(x,y) → (x+2 , y-5)

The rule of reflection across the y-axis (x,y) → (-x , y)

So, the general rule of a translation 5 units down and 2 units to the right followed by a reflection across the y-axis will be:

The rule will be (x,y) → (x+2 , y-5) → (-[x+2] , y-5)

We will check the rule:

L(2,1) → (4,-4) → (-4,4) = L'

N(1,3) → (3,-2) → (-3,-2) = N'

So, the answer is:

A translation 5 units down and 2 units to the right followed by a reflection across the y-axis