Question

Quadrilateral JKLM

is reflected over the y
-axis, rotated 180°
counterclockwise about the origin, and then translated down 5
units and right 4
units. What is the composition of functions for the given sequence of transformations?

Answer 1

The composition of functions for the given sequence of transformations is (x, y) = (x + 4, -y - 5)

What is the composition of functions for the given sequence of transformations?

From the question, we have the following parameters that can be used in our computation:

• Reflection over the y -axis
• Rotation by 180° counterclockwise about the origin
• Translation down 5 units and right 4 units

The rule of reflection over the y -axis is

(x, y) = (-x, y)

The rule of rotation by 180° counterclockwise about the origin is

(x, y) = (-x, -y)

So, we have

(x, y) = (x, -y)

The rule of translation down 5 units and right 4 units is

(x, y) = (x + 4, y - 5)

So, we have

(x, y) = (x + 4, -y - 5)

Hence, the composition of functions is (x, y) = (x + 4, -y - 5)